decoupling and simplifying of discrete dynamical systems in the

Contents

Preface 1

Organizing Committee 3

Scientific Committee 5

ISDE Advisory Committee 7

Welcome from the ISDE President 9

ISDE Board of Directors 11

Schedule 13

Monday, July 21 (One-Hour Talks) . . . . . . . . . . . . . . . . . . . . . . 15

Monday, July 21 (Contributed Talks) . . . . . . . . . . . . . . . . . . . . . 17

Tuesday, July 22 (One-Hour Talks) . . . . . . . . . . . . . . . . . . . . . . 19

Tuesday, July 22 (Contributed Talks) . . . . . . . . . . . . . . . . . . . . . 21

Thursday, July 24 (One-Hour Talks) . . . . . . . . . . . . . . . . . . . . . . 23

Thursday, July 24 (Contributed Talks) . . . . . . . . . . . . . . . . . . . . 25

Friday, July 25 (One-Hour Talks) . . . . . . . . . . . . . . . . . . . . . . . 27

Friday, July 25 (Contributed Talks) . . . . . . . . . . . . . . . . . . . . . . 29

One-Hour Speakers 31

Abstracts of One-Hour Talks 35

Agarwal, Ravi (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Akın-Bohner, Elvan (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Alseda, Lluıs (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

iii

Dosly, Ondrej (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . . . 39

Gesztesy, Fritz (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Gyori, Istvan (Hungary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Hilger, Stefan (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Kloeden, Peter (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Kocak, Huseyin (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Ladas, Gerasimos (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Mawhin, Jean (Belgium) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Peterson, Allan (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Smith, Hal (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Vanderbauwhede, Andre (Belgium) . . . . . . . . . . . . . . . . . . . . . 49

Yorke, James A. (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Zafer, Agacık (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Zeidan, Vera (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Abstracts of Contributed Talks 53

Abderraman, Jesus (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Adıvar, Murat (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Afshar Kermani, Mozhdeh (Iran) . . . . . . . . . . . . . . . . . . . . . . . 56

Aghazadeh, Nasser (Iran) . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Albayrak, Incı (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Aldea Mendes, Diana (Portugal) . . . . . . . . . . . . . . . . . . . . . . . 59

Al-Sharawi, Ziyad (Oman) . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Alzabut, Jehad (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Appleby, John (Ireland) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Aseeri, Samar (Saudi Arabia) . . . . . . . . . . . . . . . . . . . . . . . . . 63

Atasever, Nurıye (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Atay, Fatıhcan M. (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . 65

Atıcı, Ferhan (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Awerbuch Friedlander, Tamara (USA) . . . . . . . . . . . . . . . . . . . . 67

Batıt, Ozlem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Bernhardt, Chris (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

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Bodine, Sigrun (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Bolat, Yasar (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Cakmak, Devrım (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Camouzis, Elias (Greece) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Canovas, Jose S. (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Cetın, Erbıl (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Cıbıkdıken, Alı Osman (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 76

Costa, Sara (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Cushing, J. M. (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Dannan, Fozi (Syria) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Dosla, Zuzana (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . . . 80

Duman, Ahmet (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Erbe, Lynn (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Erol, Meltem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Esty, Norah (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Fernandes, Sara (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Gomes, Orlando (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Gumus, Ozlem Ak (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Guseinov, Gusein (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Guvenılır, A. Feza (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Guzowska, Małgorzata (Poland) . . . . . . . . . . . . . . . . . . . . . . . 90

Hashemiparast, Moghtada (Iran) . . . . . . . . . . . . . . . . . . . . . . . 91

Heim, Julius (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Hilscher, Roman (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . 93

Jimenez Lopez, Vıctor (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . 94

Kalabusic, Senada (Bosnia and Herzegovina) . . . . . . . . . . . . . . . . 95

Karpuz, Basak (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Keller, Christian (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Kent, Candace (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Kharkov, Vitaliy (Ukraine) . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Kipnis, Mikhail (Russia) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Kostrov, Yevgeniy (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

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Kulik, Tomasia (Australia) . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Laitochova, Jitka (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . 103

Lawrence, Bonita (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Luıs, Rafael (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Matthews, Thomas (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

McCarthy, Michael (Ireland) . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Mendes, Vivaldo (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Mert, Razıye (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Mesgarani, Hamid (Iran) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Michor, Johanna (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Migda, Małgorzata (Poland) . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Morales, Leopoldo (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Oban, Volkan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Oberste-Vorth, Ralph (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Oliveira, Henrique (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . 116

Ozturk, Rukıye (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Papaschinopoulos, Garyfalos (Greece) . . . . . . . . . . . . . . . . . . . . 118

Park, Choonkil (South Korea) . . . . . . . . . . . . . . . . . . . . . . . . . 119

Pinelas, Sandra (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Pituk, Mihaly (Hungary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Pop, Nicolae (Romania) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Popescu, Emil (Romania) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Popescu, Nedelia Antonia (Romania) . . . . . . . . . . . . . . . . . . . . . 124

Pospısil, Zdenek (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . 125

Potzsche, Christian (Germany) . . . . . . . . . . . . . . . . . . . . . . . . 126

Predescu, Mihaela (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Rabbani, Mohsen (Iran) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Rachidi, Mustapha (France) . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Radin, Michael (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Rasmussen, Martin (Germany) . . . . . . . . . . . . . . . . . . . . . . . . 131

Rehak, Pavel (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . . . 132

Reinfelds, Andrejs (Latvia) . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

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Rodkina, Alexandra (Jamaica) . . . . . . . . . . . . . . . . . . . . . . . . . 134

Romero i Sanchez, David (Spain) . . . . . . . . . . . . . . . . . . . . . . . 135

Saker, Samir (Saudi Arabia) . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Sanchez-Moreno, Pablo (Spain) . . . . . . . . . . . . . . . . . . . . . . . . 137

Schinas, Christos (Greece) . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Schmeidel, Ewa (Poland) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Sekercı, Nurcan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Shahrezaee, Mohsen (Iran) . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Siddikov, Bakhodirzhon (USA) . . . . . . . . . . . . . . . . . . . . . . . . 142

Simon, Moritz (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Sırma, Alı (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

Stefanidou, Gesthimani (Greece) . . . . . . . . . . . . . . . . . . . . . . . 145

Stehlik, Petr (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . . . . 146

Teschl, Gerald (Austria) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Tıryakı, Aydın (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Tlemcani, Mouhaydine (Portugal) . . . . . . . . . . . . . . . . . . . . . . 149

Topal, Fatma Serap (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 150

Yantır, Ahmet (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Yıldırım, Ahmet (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

Zaidi, Atiya (Australia) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Zakeri, Ali (Iran) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

Zemanek, Petr (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . . 155

Other Participants 157

Abdeljawad, Thabet (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . 158

Adıyaman, Meltem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Akman, Murat (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Altunkaynak, Meltem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 159

Aydın, Kemal (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Bas, Mujgan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Bohner, Martin (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Bozok, Ilknur (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

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Budakcı, Gulter (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Can, Canan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

Caylak, Duygu (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

Celebi, Okay (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

Celık, Cem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

Celık Kızılkan, Gulnur (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 162

Cınar, Cengız (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

Das, Sebahat Ebru (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Denız, Aslı (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Dong, Zhaoyang (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Duman, Melda (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Elaydi, Saber (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Getimane, Mario (Mozambique) . . . . . . . . . . . . . . . . . . . . . . . 164

Gumus, Ibrahım Halıl (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 165

Hatıpoglu, Veysel Fuat (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 165

Intepe, Gokce (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

Jantarakhajorn, Khajee (Thailand) . . . . . . . . . . . . . . . . . . . . . . . 166

Kara, Rukıye (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

Kayar, Zeynep (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

Kaymakcalan, Bıllur (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Kıyak Ucar, Yelız (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Kongnuan, Supachara (Thailand) . . . . . . . . . . . . . . . . . . . . . . . 167

Kosareva, Natalia (Russia) . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Kulik, Yakov (Australia) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Kutay, Vıldan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Leonhardt, Andreas (Germany) . . . . . . . . . . . . . . . . . . . . . . . . 169

Lesaja, Goran (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Marsh, Robert L. (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Mısır, Adıl (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

Nurkanovic, Mehmed (Bosnia and Herzegovina) . . . . . . . . . . . . . . 170

Nurkanovic, Zehra (Bosnia and Herzegovina) . . . . . . . . . . . . . . . . 170

Ocalan, Ozkan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

viii

Okumus, Israfıl (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

Ozkan, Umut Mutlu (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . 171

Ozpınar, Fıgen (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

Ozturk, Sermın (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

Ozugurlu, Ersın (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

Reankittiwat, Paramee (Thailand) . . . . . . . . . . . . . . . . . . . . . . . 173

Ruffing, Andreas (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Savun, Ipek (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Selmanogulları, Tugcen (Turkey) . . . . . . . . . . . . . . . . . . . . . . . 174

Seneetantikul, Soporn (Thailand) . . . . . . . . . . . . . . . . . . . . . . . 174

Seyhan, Gızem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Sımsek, Dagıstan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Sizer, Walter (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Suhrer, Andreas (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Taskara, Necatı (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Thongjub, Nawalax (Thailand) . . . . . . . . . . . . . . . . . . . . . . . . 176

Tollu, D. Turgut (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Ucar, Denız (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Unal, Mehmet (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Vesarachasart, Sirichan (Thailand) . . . . . . . . . . . . . . . . . . . . . . 177

Vu, Dominik (Austria) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Yalazlar, Gulcın (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Yalcınkaya, Ibrahım (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . 178

Yıgıder, Muhammed (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . 179

Yıldız, Mustafa Kemal (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 179

Yılmaz, Ozlem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Yoruk, Fulya (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

Local Organization Assistants 181

Aydın, M. Aslı (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Bayat, Kemal (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Dagyar, Nazlı Ceren (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . 182

ix

Emul, Yakup (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Erkal, Durdane (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Karahan, Gokce (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Karakelle, Musa (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Ozdemır, Huseyın (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Ozen, Bahadır (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Conference Proceedings 185

Social Program 187

Maps 189

Istanbul 197

Useful Information 205

Index and E-mail Addresses 209

x

Preface

Dear Colleague:

It is our great pride and pleasure to offer ourwarmest greetings to you, the participants of the “14thInternational Conference on Difference Equations andApplications (ICDEA2008)” at the Besiktas campus ofBahcesehir University in Istanbul, Turkey. This confer-ence is sponsored by TUBITAK (Scientific and Tech-nical Research Council of Turkey), Bahcesehir Univer-sity, Dentur Avrasya, Duran Sandwiches, Pırıl Pırıl,and the Turkish Ministry of Culture and Tourism.

The purpose of the conference is to bring together both experts and novicesin the theory and applications of difference equations and discrete dynamicalsystems. The main theme of the meeting is dynamic equations on time scales.The previous ICDEA conferences were held in Lisbon (2007), Kyoto (2006), Mu-nich (2005), Los Angeles (2004), Brno (2003), Changsha (2002), Augsburg (2001),Temuco (2000), Poznan (1998), Taipei (1997), Veszprem (1995), and San Antonio(1994).

In addition to attending the conference’s exciting sessions, we encourageeach of the participants to take advantage of our historic city of Istanbul, whichis the cradle of many civilizations, to share beauty and scientific knowledge. Lastbut not least we want to extend our best wishes to all of the conference partici-pants and to its Scientific and Organizing Committee members.

Sincerely,

Dr. Mehmet UnalChair of Organizing CommitteeBahcesehir UniversityTR-34538 Bahcesehir/Istanbul, Turkey

Conference web site: http://icdea.bahcesehir.edu.tr

1

Organizing Committee

Mehmet Unal (Chair)Bahcesehir University

Istanbul, Turkey

Martin Bohner (Co-Chair)Missouri S&T

Rolla, Missouri, USA

Okay CelebiYeditepe University

Istanbul, Turkey

Gerasimos LadasUniversity of Rhode Island

Kingston, Rhode Island, USA

Aydın TıryakıGazi UniversityAnkara, Turkey

Agacık ZaferMiddle East Technical University

Ankara, Turkey

3

Scientific Committee

Martin Bohner (Chair)Missouri S&T


Zuzana Dosla (Co-Chair)Masaryk University

Brno, Czech Republic

Saber ElaydiTrinity University

San Antonio, Texas, USA

Metin GursesBilkent University

Ankara, Turkey

Gusein GuseinovAtılım UniversityAnkara, Turkey

Bıllur KaymakcalanGeorgia Southern University

Statesboro, Georgia, USA

Peter KloedenJohann Wolfgang Goethe University

Frankfurt am Main, Germany

5

Werner KratzUniversity of Ulm

Ulm, Germany

Donald LutzSan Diego State UniversitySan Diego, California, USA

Jean MawhinUniversite Catholique de Louvain

Louvain-la-Neuve, Belgium

Donal O’ReganNational University of Ireland

Galway, Ireland

Allan PetersonUniversity of Nebraska–Lincoln

Lincoln, Nebraska, USA

Alexander SharkovskyNational Academy of Sciences

Kiev, Ukraine

Gerald TeschlUniversity of Vienna

Vienna, Austria

6

ISDE Advisory Committee

Kazuo Nishimura (Chair)Kyoto University

Kyoto, Japan

Andreas Ruffing (Co-Chair)Technical University Munich

Munich, Germany

Henrique OliveiraInstituto Superior Tecnico Lisbon

Lisbon, Portugal

Robert J. SackerUniversity of Southern California

Los Angeles, California, USA

7

Welcome from the ISDE President

Dear Colleagues and ISDE Members:

It is an honor to welcome you to the annual meet-ing of the International Society of Difference Equa-tions in Istanbul, Turkey. The Fourteenth InternationalConference on Difference Equations and ApplicationsICDEA2008 is held on the campus of Bahcesehir Uni-versity, July 21–25, 2008.

I welcome you to this historical meeting, wherewest meets east; you may be able to cross on foot from Asia to Europe and viceversa. Not only we have an excellent scientific program, but we have a splendidsocial program; don’t forget your camera.

The ISDE Board of Directors meets on Tuesday, July 22th, 2008, 5:45 pm in theauditorium BFSAY. The general assembly of the society meets on Thursday, July24th, 2008, 5:45 pm in the auditorium BFSAY. The main event is the presentationof the prize for the best paper published in the Journal of the Society (JDEA) in2007. The prize carries the amount of £500 granted by Taylor & Francis.

Finally, I would like to thank, on behalf of all of you, Dr. Mehmet Unal of theUniversity of Bahcesehir for his relentless efforts to make ICDEA2008 a reality. Iam grateful to all members of the organizing, scientific, and advisory committeesfor their hard work and efforts to make this conference the best it can be.

Sincerely,

Dr. Saber ElaydiPresident of ISDETrinity University


9

ISDE Board of Directors

Saber Elaydi (President)Trinity University


George Sell (Vice President)University of Minnesota

Minneapolis, Minnesota, USA

Martin BohnerMissouri S&T


J. M. CushingUniversity of ArizonaTucson, Arizona, USA

Istvan GyoriUniversity of Pannonia

Veszprem, Hungary

11





Andreas RuffingTechnical University Munich

Munich, Germany

Robert J. SackerUniversity of Southern California

Los Angeles, California, USA

12

Schedule

13

Time July 20 July 21 July 22 July 23 July 24 July 25

Sunday Monday Tuesday Wednesday Thursday Friday

8:00–9:00 Registration Istanbul

9:00–9:45 Opening Tour

9:45–10:40 Plenary Talk Plenary Talk Plenary Talk Plenary Talk

1 3 Istanbul 5 710:45–11:00 Refreshment Break Tour Refreshment Break

11:00–11:55 Plenary Talk Plenary Talk Plenary Talk Plenary Talk

2 4 Istanbul 6 812:00–13:00 Lunch Tour Lunch

13:00–13:55 Main Talks Main Talks Main Talks Plenary Talk

1–3 4–6 Istanbul 7–8 914:00–14:25 Registration Talks Talks Tour Talks Talks

1–4 29–32 57–60 81–8414:30–14:55 Talks Talks Istanbul Talks Talks

5–8 33–36 Tour 61–64 85–8815:00–15:25 Talks Talks Talks Talks

9–12 37–40 Istanbul 65–68 89–9215:25–16:15 Registration Refreshment Break Tour Refreshment Break

16:15–16:40 Talks Talks Talks Talks

13–16 41–44 Istanbul 69–72 93–9616:45–17:10 Talks Talks Tour Talks Talks

17–20 45–48 73–76 97–10017:15–17:40 Registration Talks Talks Istanbul Talks Closing

21–24 49–52 Tour 77–8017:45–18:10 Talks Talks ISDE

25–28 53–56 Yacht Meeting

Evening Welcome Sightseeing Sightseeing Tour Farewell Sightseeing

Party free time free time Dinner free time

14

Monday, July 21 (One-Hour Talks)

Time BFSAY A101 A205

8:00–9:00 Registration

9:00–9:45 Opening

Chair M. Bohner

9:45–10:40

AllanPeterson

(USA)page 47

10:45–11:00 Refreshment Break

11:00–11:55

RaviAgarwal

(USA)page 36

12:00–13:00 Lunch Break

Chair G. Ladas R. Hilscher B. Kaymakcalan

13:00–13:55

IstvanGyori

(Hungary)page 41

VeraZeidan(USA)

page 52

StefanHilger

(Germany)page 42

15

? Agarwal, Ravi: Discrete Lidstone boundary value problems

? Gyori, Istvan: Asymptotic representation of solutions of difference equations and limitformulas

? Hilger, Stefan: Difference equations appearing in ladder theory

? Peterson, Allan: An overview of dynamic equations on time scales

? Zeidan, Vera: Variational problems over time scales

16

Monday, July 21 (Contributed Talks)

Time A101 A205 A206 A207

Chair V. Zeidan C. Kent J. Appleby N. Aghazadeh

14:00–14:25

RomanHilscher

(Czech Republic)page 93

TamaraAwerbuch Friedlander

(USA)page 67

OrlandoGomes

(Portugal)page 86

NicolaePop

(Romania)page 122

14:30–14:55

LynnErbe

(USA)page 82

MihaelaPredescu

(USA)page 127

VivaldoMendes

(Portugal)page 108

VolkanOban

(Turkey)page 114

15:00–15:25

NorahEsty

(USA)page 84

GaryfalosPapaschinopoulos

(Greece)page 118

SenadaKalabusic

(Bosnia/Herz.)page 95

BakhodirzhonSiddikov

(USA)page 142


Chair S. Bodine E. Camouzis L. Alseda N. Popescu

16:15–16:40

RalphOberste-Vorth

(USA)page 115

ChristosSchinas(Greece)page 138

DianaAldea Mendes

(Portugal)page 59

IncıAlbayrak(Turkey)page 58

16:45–17:10

AhmetYantır

(Turkey)page 151

VıctorJimenez Lopez

(Spain)page 94

ChrisBernhardt

(USA)page 69

MohsenShahrezaee

(Iran)page 141

17:15–17:40

PetrStehlik


SandraPinelas

(Portugal)page 120

Jose S.Canovas(Spain)page 74

MoghtadaHashemiparast

(Iran)page 91

17:45–18:10

MuratAdıvar

(Turkey)page 55

NurıyeAtasever(Turkey)page 64

SaraCosta

(Spain)page 77

NasserAghazadeh

(Iran)page 57

17

? Adıvar, Murat: Periodicity in nonlinear systems of dynamic equations? Aghazadeh, Nasser: Using B-spline scaling functions for solving integro-differential equa-

tions? Albayrak, Incı: A trace formula for an abstract Sturm–Liouville operator? Aldea Mendes, Diana: Periodic and eventually periodic orbits for skew-product maps? Atasever, Nurıye: On a class of rational difference equations? Awerbuch Friedlander, Tamara: Constructing difference equations models for public health

policy? Bernhardt, Chris: A Sharkovsky theorem for maps on trees? Canovas, Jose S.: A characterization of k-cycles? Costa, Sara: Study of attractors for two-dimensional skew-products whose basis is a Den-

joy counterexample? Erbe, Lynn: Comparison and oscillation theorems for linear and half-linear dynamic equa-

tions on time scales? Esty, Norah: Convergence of hyperspaces under the Fell topology, especially of time scales? Gomes, Orlando: Optimal monetary policy with partially rational agents? Hashemiparast, Moghtada: Solving systems of nonlinear equations by using difference

equations? Hilscher, Roman: Riccati equations for linear Hamiltonian systems? Jimenez Lopez, Vıctor: On the global stability of xn+1 = p+qxn

1+xn−1

? Kalabusic, Senada: Period-two trichotomies of a difference equation of order higher thantwo

? Mendes, Vivaldo: Learning to play Nash in deterministic uncoupled dynamics? Oban, Volkan: Numerical solutions of nonlinear differential-difference equations by the

variational iteration method? Oberste-Vorth, Ralph: Solution spaces of dynamic equations over time scales space? Papaschinopoulos, Garyfalos: Boundedness, attractivity, stability of a rational difference

equation with two periodic coefficients? Pinelas, Sandra: Bounded solutions of a rational difference equation? Pop, Nicolae: Generalized Jacobians for solving nondifferentiable equations arising from

contact problems? Predescu, Mihaela: A nonlinear system of difference equations? Schinas, Christos: Boundedness, periodicity, attractivity of the difference equation xn+1 =An +

(xn−1xn

)p

? Shahrezaee, Mohsen: Heat solutions by using Fibonacci tane function? Siddikov, Bakhodirzhon: Applications of finite difference methods in the field of magnetic

refrigeration? Stehlik, Petr: Basic properties of partial dynamic operators? Yantır, Ahmet: Positive solutions of a second-order m-point BVP on time scales

18

Tuesday, July 22 (One-Hour Talks)

Time BFSAY A101 A205

Chair Z. Dosla

9:45–10:40

HuseyinKocak(USA)

page 44


11:00–11:55

AndreVanderbauwhede

(Belgium)page 49


Chair C. Potzsche A. Peterson G. Teschl

13:00–13:55

LluısAlseda(Spain)page 38

ElvanAkın-Bohner

(USA)page 37

FritzGesztesy

(USA)page 40

19

? Alseda, Lluıs: A lower bound for the maximum topological entropy of 4k + 2-cycles

? Akın-Bohner, Elvan: Quasilinear dynamic equations

? Gesztesy, Fritz: Borg–Marchenko-type uniqueness results for CMV operators and elementsof Weyl–Titchmarsh theory

? Kocak, Huseyin: Rigorous computations in chaotic dynamical systems

? Vanderbauwhede, Andre: Stability of bifurcating periodic orbits of reversible maps

20

Tuesday, July 22 (Contributed Talks)

Time A101 A205 A206 A207

Chair F. Atıcı S. Pinelas M. Rasmussen V. Mendes

14:00–14:25

ThomasMatthews

(USA)page 106

EliasCamouzis(Greece)page 73

SaraFernandes(Portugal)

page 85

JohnAppleby(Ireland)page 62

14:30–14:55

JuliusHeim(USA)

page 92

YevgeniyKostrov(USA)

page 101

LeopoldoMorales(Spain)

page 113

AlexandraRodkina(Jamaica)page 134

15:00–15:25

BonitaLawrence

(USA)page 104

MustaphaRachidi(France)page 129

HenriqueOliveira

(Portugal)page 116

MichaelMcCarthy(Ireland)page 107


Chair L. Erbe M. Predescu H. Oliveira A. Rodkina

16:15–16:40

TomasiaKulik

(Australia)page 102

MichaelRadin(USA)

page 130

ChristianPotzsche

(Germany)page 126

JitkaLaitochova


16:45–17:10

ChristianKeller(USA)

page 97

CandaceKent

(USA)page 98

AndrejsReinfelds(Latvia)page 133

JesusAbderraman

(Spain)page 54

17:15–17:40

AtiyaZaidi

(Australia)page 153

GesthimaniStefanidou

(Greece)page 145

MartinRasmussen(Germany)page 131

Alı OsmanCıbıkdıken

(Turkey)page 76

17:45–18:10

FerhanAtıcı

(USA)page 66

NurcanSekercı(Turkey)page 140

MouhaydineTlemcani(Portugal)page 149

AhmetDuman(Turkey)page 81

21

? Abderraman, Jesus: General solution of linear homogeneous difference equations withvariable coefficients

? Appleby, John: Growth, long memory and heavy tails in difference equation models ofinefficient financial markets

? Atıcı, Ferhan: Initial value problems in discrete fractional calculus? Camouzis, Elias: On the global character of solutions of a rational system of difference

equations? Cıbıkdıken, Alı Osman: Effect of floating point on computation of monodromy matrix? Duman, Ahmet: Sensitivity of Schur stable linear systems with periodic coefficients? Fernandes, Sara: Systoles and topological entropy in discrete dynamical systems? Heim, Julius: The dynamic multiplier-accelerator model in economics? Keller, Christian: Dynamic equations with piecewise continuous argument? Kent, Candace: A cardiac loop reentry model with thresholds? Kostrov, Yevgeniy: Existence of unbounded solutions in rational equations? Kulik, Tomasia: Solution to integral equations on time scales: Existence, uniqueness and

successive approximations? Laitochova, Jitka: Linear kth order functional and difference equations in the space of

strictly monotonic functions? Lawrence, Bonita: The Marshall differential analyzer: Dynamic equations in motion!? Matthews, Thomas: Ostrowski inequalities on time scales? McCarthy, Michael: Numerical detection of explosions and asymptotic behaviour of delay-

differential equations? Morales, Leopoldo: An example of a strongly invariant, pinched core strip? Oliveira, Henrique: Bifurcations for nonautonomous interval maps? Potzsche, Christian: Nonautonomous continuation and bifurcation, revisited!? Rachidi, Mustapha: On some rational difference equations via linear recurrence equations

properties? Radin, Michael: Multiple periodic solutions of a second-order nonautonomous rational

difference equation? Rasmussen, Martin: Morse spectrum for linear nonautonomous difference equations? Reinfelds, Andrejs: Decoupling and simplifying of discrete dynamical systems in the neigh-

bourhood of invariant manifold? Rodkina, Alexandra: On oscillation of solutions of stochastically perturbed difference equa-

tions? Sekercı, Nurcan: On the behaviour of the difference equationx(n+ 1) = max1/x(n),min1, A/x(n)

? Stefanidou, Gesthimani: On a system of max-difference equations? Tlemcani, Mouhaydine: Analysis of a nonlinear discrete dynamical system, signal coding

and reconstruction? Zaidi, Atiya: A result on successive approximation of solutions to dynamic equations on

time scales

22

Thursday, July 24 (One-Hour Talks)

Time BFSAY A101

Chair J. Cushing

9:45–10:40

James A.Yorke(USA)

page 50


11:00–11:55

HalSmith(USA)

page 48


Chair F. Gesztesy B. Lawrence

13:00–13:55

JeanMawhin(Belgium)page 46

AgacıkZafer

(Turkey)page 51

23

? Mawhin, Jean: Boundary value problems for nonlinear difference equations with discretesingular φ-Laplacian

? Smith, Hal: Some persistence results for discrete-time dynamical systems and applications

? Yorke, James A.: Period doubling cascades in one-parameter families of maps in high di-mensions

? Zafer, Agacık: Interval criteria for second-order super-half-linear functional dynamic equa-tions

24

Thursday, July 24 (Contributed Talks)

Time A101 A205 A206 A207

Chair N. Esty S. Hilger T. Awerbuch Friedlander A. Tıryakı

14:00–14:25

DevrımCakmak(Turkey)page 72

ZuzanaDosla


MoritzSimon

(Germany)page 143

MikhailKipnis(Russia)page 100

14:30–14:55

PavelRehak


VitaliyKharkov(Ukraine)page 99

MałgorzataGuzowska

(Poland)page 90

Ozlem AkGumus(Turkey)page 87

15:00–15:25

RazıyeMert

(Turkey)page 109

GuseinGuseinov(Turkey)page 88

RafaelLuıs

(Portugal)page 105

ChoonkilPark

(South Korea)page 119


Chair M. Adıvar J. Michor A. Reinfelds G. Guseinov

16:15–16:40

BasakKarpuz(Turkey)page 96

MihalyPituk

(Hungary)page 121

ZiyadAl-Sharawi

(Oman)page 60

JehadAlzabut(Turkey)page 61

16:45–17:10

ErbılCetın

(Turkey)page 75

GeraldTeschl

(Austria)page 147

J. M.Cushing

(USA)page 78

AydınTıryakı(Turkey)page 148

17:15–17:40

ZdenekPospısil


RukıyeOzturk

(Turkey)page 117

FoziDannan(Syria)page 79

SigrunBodine(USA)

page 70

17:45–18:10 ISDE General Meeting (BFSAY)

25

? Al-Sharawi, Ziyad: The effect of harvesting strategies on the discrete Beverton–Holt model

? Alzabut, Jehad: Asymptotic behavior of linear impulsive delay difference equations

? Bodine, Sigrun: Exponentially asymptotically constant systems of difference equationswith applications

? Cakmak, Devrım: On the equivalence of Rolle’s and generalized mean value theorems ontime scales

? Cetın, Erbıl: Higher-order boundary value problems on time scales

? Cushing, J. M.: Difference equations arising in dynamic models of biological evolution

? Dannan, Fozi: A new proof for the Levin–May criterion of asymptotic stability

? Dosla, Zuzana: On nonoscillation of Emden–Fowler difference equations

? Gumus, Ozlem Ak: Stability boundary for asymptotic stability of scalar equations

? Guseinov, Gusein: Spectral analysis of a non-selfadjoint second-order difference operator

? Guzowska, Małgorzata: Discrete Haavelmo growth cycle model

? Karpuz, Basak: Iterated oscillation criteria for delay dynamic equations of first order

? Kharkov, Vitaliy: Asymptotic behavior of one class solutions of the second-order Emden–Fowler difference equation

? Kipnis, Mikhail: Stability via Convexity

? Luıs, Rafael: Nonautonomous periodic systems with Allee effect

? Mert, Razıye: Time scale extensions of a theorem of Wintner on systems with asymptoticequilibrium

? Ozturk, Rukıye: On the spectrum of normal difference operators of first order

? Park, Choonkil: Classification and stability of functional equations

? Pituk, Mihaly: Nonoscillatory solutions of a second-order difference equation of Poincaretype

? Pospısil, Zdenek: Dynamic replicator equation and its transformation

? Rehak, Pavel: Power type comparison theorems for half-linear dynamic equations

? Simon, Moritz: Spectral theory of birth-and-death processes

? Teschl, Gerald: Relative oscillation theory for Jacobi operators

? Tıryakı, Aydın: Reducibility and stability results for linear systems of difference equations

26

Friday, July 25 (One-Hour Talks)

Time BFSAY

Chair O. Celebi

9:45–10:40

OndrejDosly



11:00–11:55

PeterKloeden

(Germany)page 43


13:00–13:55

GerasimosLadas(USA)

page 45

27

? Dosly, Ondrej: Symplectic difference systems

? Kloeden, Peter: Spatial discretisation of dynamical systems

? Ladas, Gerasimos: Open problems and conjectures in difference equations

28

Friday, July 25 (Contributed Talks)

Time A101 A205 A206 A207

Chair A. Zafer M. Pituk B. Siddikov J. Laitochova

14:00–14:25

OzlemBatıt

(Turkey)page 68

MałgorzataMigda

(Poland)page 112

Nedelia AntoniaPopescu

(Romania)page 124

JohannaMichor(USA)

page 111

14:30–14:55

PetrZemanek


EwaSchmeidel

(Poland)page 139

DavidRomero i Sanchez

(Spain)page 135

PabloSanchez-Moreno

(Spain)page 137

15:00–15:25

Fatma SerapTopal

(Turkey)page 150

YasarBolat

(Turkey)page 71

AlıSırma

(Turkey)page 144

SamarAseeri

(Saudi Arabia)page 63


Chair F. Topal O. Ocalan A. Sırma S. Aseeri

16:15–16:40

MozhdehAfshar Kermani

(Iran)page 56

A. FezaGuvenılır(Turkey)page 89

AhmetYıldırım(Turkey)page 152

MeltemErol

(Turkey)page 83

16:45–17:10

Fatıhcan M.Atay

(Germany)page 65

MohsenRabbani

(Iran)page 128

AliZakeri(Iran)

page 154

HamidMesgarani

(Iran)page 110

17:15–17:40 Closing (BFSAY)

29

? Afshar Kermani, Mozhdeh: A new method for solving fuzzy partial differential equations

? Aseeri, Samar: Asymptotic formulas for Laplace integrals

? Atay, Fatıhcan M.: Stability of coupled difference equations with delays

? Batıt, Ozlem: Fredholm integral equations on time scales

? Bolat, Yasar: Necessary and sufficient conditions for oscillation of certain higher orderpartial difference equations

? Erol, Meltem: The structure of the spectrum for normal operators

? Guvenılır, A. Feza: Interval oscillation of second-order difference equations with oscilla-tory potentials

? Mesgarani, Hamid: A new approach for solving Fredholm integro-difference equations

? Michor, Johanna: Algebro-geometric solutions of the Ablowitz–Ladik hierarchy

? Migda, Małgorzata: Oscillatory and asymptotic properties of solutions of nonlinear neutral-type difference equations

? Popescu, Nedelia Antonia: Finite size scaling technique and applications

? Rabbani, Mohsen: Galerkin method for solving nonlinear Fredholm–Hammerstein integralequations with multiwavelet basis

? Romero i Sanchez, David: Invariant objects through wavelets

? Sanchez-Moreno, Pablo: Discrete densities and Fisher information

? Schmeidel, Ewa: Oscillation of nonlinear three-dimensional difference systems

? Sırma, Alı: Numerical solution of nonlocal boundary value problems for the Schrodingerequation

? Topal, Fatma Serap: Multiple positive solutions for a system of higher-order boundaryvalue problems on time scales

? Yıldırım, Ahmet: Numerical solutions of nonlinear differential-difference equations by thehomotopy perturbation method

? Zakeri, Ali: Application of the WKB estimation method for determining heat flux on theboundary

? Zemanek, Petr: Trigonometric and hyperbolic systems on time scales

30

One-Hour Speakers

Ravi AgarwalFlorida Institute of Technology

Melbourne, Florida, USA

Elvan Akın-BohnerMissouri S&T


Lluıs AlsedaUniversitat Autonoma de Barcelona

Cerdanyola del Valles, Spain

Ondrej DoslyMasaryk University


Fritz GesztesyUniversity of Missouri

Columbia, Missouri, USA

Istvan GyoriUniversity of Pannonia

Veszprem, Hungary

31

Stefan HilgerCatholic University of Eichstatt

Eichstatt, Germany

Peter KloedenJohann Wolfgang Goethe University


Huseyin KocakUniversity of MiamiMiami, Florida, USA



Jean MawhinUniversite Catholique de Louvain




32

Hal SmithArizona State University

Tempe, Arizona, USA

Andre VanderbauwhedeGhent UniversityGhent, Belgium

James A. YorkeUniversity of Maryland

College Park, Maryland, USA


Ankara, Turkey

Vera ZeidanMichigan State University

East Lansing, Michigan, USA

33

Abstracts of One-Hour Talks

35

Discrete Lidstone boundary value problems

RAVI AGARWAL

Florida Institute of Technology

Department of Mathematics

Melbourne, Florida, USA

[email protected]

http://cos.fit.edu/math/faculty/agarwal

We shall provide sufficient conditions for the existence of single and multiple positive solu-tions of higher order smooth as well as singular difference equations involving Lidstone bound-ary conditions. As an application, we shall investigate the existence of radial solutions of certainpartial difference equations. To show how easily our results can be applied in practice we shallillustrate many examples.

36

Quasilinear dynamic equations

ELVAN AKIN-BOHNER

Missouri University of Science and Technology

Department of Mathematics and Statistics


[email protected]

http://web.mst.edu/˜akine

We consider a quasilinear dynamic equation reducing to a half-linear equation, Emden–Fowler equation or a Sturm–Liouville equation on a time scale, which is a nonempty closed subsetof the real numbers. Any nontrivial solution of a quasilinear equation is eventually monotone. Inother words, it can be either positive decreasing (negative increasing) or positive increasing (neg-ative decreasing). We shall provide certain integral conditions to classify solutions and investigatetheir asymptotic behaviors.

AMS Subject Classification: 39A10.Keywords: Time scales, quasilinear, half-linear equation.

37

A lower bound for the maximum

topological entropy of 4k + 2-cycles

LLUIS ALSEDA

Universitat Autonoma de Barcelona

Departament de Matematiques

Cerdanyola del Valles, Spain

[email protected]

http://www.mat.uab.cat/˜alseda

For continuous interval maps we formulate a conjecture on the shape of the cycles of maxi-mum topological entropy of period 4k + 2. We also present numerical support for the conjecture.This numerical support is of two different kinds. For periods 6, 10, 14 and 18 we are able tocompute the maximum entropy cycles by using nontrivial, ad hoc numerical procedures and theknown results of Jungreis (1991). In fact, the conjecture we formulate is based on these results.

For periods n = 22, 26 and 30 we compute the maximum entropy cycle of a restricted sub-family of cycles denoted by C∗n. The obtained results agree with the conjectured ones. The con-jecture that we can restrict our attention to C∗n is motivated theoretically. On the other hand, it isworth noticing that the complexity of examining all cycles in C∗22, C∗26 and C∗30 is much less thanthe complexity of computing the entropy of each cycle of period 18 in order to determine the oneswith maximal entropy, therefore making it a feasible problem.

AMS Subject Classification: 37B40, 37E15, 37M99.Keywords: Combinatorial dynamics, interval map.This is joint work with David Juher and Deborah King.

38

Symplectic difference systems

ONDREJ DOSLY

Masaryk University



[email protected]

http://www.muni.cz/people/Ondrej.Dosly

Symplectic diference systems are first order systems with the property that their fundamen-tal matrix is symplectic whenever it is symplectic at one point. From this point of view, they canbe regarded as a discrete counterpart of linear Hamiltonian differential systems.

Symplectic systems cover a large variety of difference equations and systems, among themthe second order Sturm–Liouville difference equation whose oscillation theory is deeply devel-oped. We will present recent results of the oscillation and spectral theory of symplectic systems.In particular, it will be shown that the classical Sturmian separation and comparison theory canbe extended to symplectic systems.

The presented results have been achieved in the joint research with Martin Bohner (Univ.Rolla, Missouri, USA) an Werner Kratz (Univ. Ulm, Germany).

AMS Subject Classification: 39A10.Keywords: Sturmian theory, focal point, Picone’s identity.

39

Borg–Marchenko-type uniqueness results for CMV

operators and elements of Weyl–Titchmarsh theory

FRITZ GESZTESY

University of Missouri


Columbia, Missouri, USA

[email protected]

http://www.math.missouri.edu/˜fritz

We review local and global versions of Borg–Marchenko-type uniqueness theorems for half-lattice and full-lattice CMV operators (CMV for Cantero, Moral, and Velazquez) with matrix-valued Verblunsky coefficients. While our half-lattice results are formulated in terms of matrix-valued Weyl–Titchmarsh functions, our full-lattice results involve the diagonal and main off-diagonal Green’s matrices.

We also hint at the basics of Weyl–Titchmarsh theory for CMV operators with matrix-valuedVerblunsky coefficients as this is of independent interest and an essential ingredient in provingthe corresponding Borg–Marchenko-type uniqueness theorems.

This is based on joint work with Steve Clark and Maxim Zinchenko.

AMS Subject Classification: Primary 34E05, 34B20, 34L40; Secondary 34A55.Keywords: CMV operators, (inverse) spectral theory.

40

Asymptotic representation of solutions of

difference equations and limit formulas

ISTVAN GYORI

University of Pannonia

Department of Mathematics and Computing

Veszprem, Hungary

[email protected]

http://www.szt.vein.hu/˜gyori

In this lecture we investigate the growth/decay rate of solutions of linear and quasilineardifference equations. The results can be applied to a particular kind of weight sequences whichcan be either exponential or slowly decaying. Examples are given to illustrate the sharpness ofthe results.

AMS Subject Classification: 39A12.Keywords: Limit formulas, difference equations.

41

Difference equations appearing in ladder theory

STEFAN HILGER

Catholic University of Eichstatt

Mathematisch-Geographische Fakultat

Eichstatt, Germany

[email protected]

http://www.ku-eichstaett.de/Fakultaeten/MGF/

→Didaktiken/dphys/Mitarbeiter.de

A ladder consists of a sequence of vector spaces (Vn) and linear operators (A+n ), (A−n ), de-

pending on n, acting between these vector spaces in ascending and descending direction. Thejob in ladder theory is to find SIE-subladders, on which the intrinsic endomorphisms A−nA+

n andA+

nA−n act as scalars αn. A fundamental ladder theorem will provide conditions on the (gener-

alized) commutators or anticommutators assuring the existence of SIE-subladders. Elementarydifference operators will enter into those conditions. The second part contains examples of lad-ders from classical quantum mechanics or orthogonal polynomials. In a final part we point outhow to generalize the notion of a ladder to higher dimensional settings with corresponding bidi-rectional operators.

AMS Subject Classification: 81S05, 39A10, 42C05, 46L65, 34L40.Keywords: Ladder theory, canonical commutator relations.

42

Spatial discretisation of dynamical systems

PETER KLOEDEN

Johann Wolfgang Goethe University



[email protected]

http://www.math.uni-frankfurt.de/˜numerik/kloeden

We consider the effects of spatial discretisation on the dynamical behavior of discrete timedynamical systems which are generated by difference equations. This is important, for examplewhen we simulate such systems on computers which have only finite number fields. What is theffect of round-off? A simple example is the chaotic behavior of the tent mapping on the unitinterval, which collapses when the mapping is restricted to a the subset of N -dyadic numbers.We will show that invariant measures are more robust to approximation. We consider a Lebesguemeasure preserving mapping on torus and its approximation by a permutation of a uniform gridon the torus. Then, more generally, we show how Markov chains can be used to obtain approxi-mations to the invariant measures of discrete time dynamical systems.

Keywords: Discretisation, invariant measures, Markov chains.

43

Rigorous computations in chaotic dynamical systems

HUSEYIN KOCAK

University of Miami

Department of Mathematics / Department of Computer Science

Miami, Florida, USA

[email protected]

http://www.math.miami.edu/˜hk

Numerical simulations are indespensible in the investigation of specific dynamical systems.Unfortunately, since chaotic dynamical systems amplify small errors at an exponential rate, theresults of most simulations are unreliable. In this talk, we will descibe the medhod of shadowingfor extracting mathematically rigorous results from numerical computations. In particular, wewill present a computer-assisted procedure for proving the existence of transversal homoclinicand heteroclinic orbits. The talk will be illustrated with computer simulations.

44

Open problems and conjectures

in difference equations

GERASIMOS LADAS

University of Rhode Island



[email protected]

http://www.math.uri.edu/˜gladas

We present some open problems and conjectures about some interesting types of differenceequations. We are primarily interested in the boundedness nature of solutions, the periodic char-acter of the equation, the global stability behavior of the equilibrium points, and with convergenceto periodic solutions including periodic trichotomies.

45

Boundary value problems for nonlinear difference

equations with discrete singular φ-Laplacian

JEAN MAWHIN

Universite Catholique de Louvain



[email protected]

We study the existence and multiplicity of solutions for boundary value problems of the type

∇[φ(∆xk)] + fk(xk,4xk) = 0 (2 ≤ k ≤ n− 1), l(x,4x) = 0,

where φ : (−a, a) → R denotes an increasing homeomorphism such that φ(0) = 0 and 0 <

a < ∞, l(x,4x) = 0 denotes the Dirichlet, periodic or Neumann boundary conditions and fk

(2 ≤ k ≤ n − 1) are continuous functions. Our main tool is Brouwer degree together with fixedpoint reformulations of the above problems.

AMS Subject Classification: 39A12, 55M25.Keywords: Nonlinear difference equations, φ-Laplacian.This is joint work with Cristian Bereanu.

46

An overview of dynamic equations on time scales

ALLAN PETERSON

University of Nebraska–Lincoln



[email protected]

http://www.math.unl.edu/˜apeterson1

The talk will be an overview of dynamic equations on time scales. We will discuss the im-portance of this emerging area of mathematics and discuss some important results in this area.Some introductory results will also be presented.

AMS Subject Classification: 39.Keywords: Time scales, dynamic equations.

47

Some persistence results for discrete-time

dynamical systems and applications

HAL SMITH

Arizona State University


Tempe, Arizona, USA

[email protected]

http://math.la.asu.edu/˜halsmith

The theory of persistence focuses on identifying sufficient conditions for certain subsets ofthe state space to be repellers for the considered dynamics. In an ecological setting, these subsetsare often extinction states for one or more populations while in an epidemiological setting theymay be disease-free states. We survey some recent results in this area and apply them to modelsin population biology and epidemiology.

Keywords: Persistence theory.

48

Stability of bifurcating periodic

orbits of reversible maps

ANDRE VANDERBAUWHEDE

Ghent University


Ghent, Belgium

[email protected]

http://cage.ugent.be/˜avdb

The Lyapunov–Schmidt method for the bifurcation of periodic orbits of local diffeomor-phisms results in a reduced problem with an additional cyclic symmetry. We show how themethod can be refined such that it also gives information on the stability of the bifurcating pe-riodic orbits. We apply this approach (via a Poincare map) to the problem of subharmonic bi-furcations in continuous reversible systems, discussing both the generic case and a particulardegenerate case. A numerical study of a model example for this degenerate situation revealssome nongeneric stability behaviour in the presence of certain first integrals. We describe theresults of a detailed analysis for this conservative case, including the transition scenario to thenonconservative case.

This is joint work with Francisco Javier Munoz-Almaraz (Valencia), and Jorge Galan andEmilio Freire (Sevilla).

49

Period doubling cascades in one-parameter

families of maps in high dimensions

JAMES A. YORKE

University of Maryland


College Park, Maryland, USA

[email protected]

http://yorke.umd.edu

Evelyn Sander and I show infinite period-doubling cascades exist for high-dimensional sys-tems.

50

Interval criteria for second-order super-half-linear

functional dynamic equations

AGACIK ZAFER

Middle East Technical University


Ankara, Turkey

[email protected]

http://www.metu.edu.tr/˜zafer

Interval oscillation criteria are established for second-order forced super half-linear dynamicequations on time scales containing both delay and advance arguments, where the potentialsare allowed to change sign. Examples are given to illustrate the relevance of the results. Thetheory can be applied to second-order dynamic equations regardless of the choice of delta ornabla derivatives.

AMS Subject Classification: 34K11, 34C10, 39A11, 39A13.Keywords: Time scales, oscillation, functional, half-linear.This is joint work with Douglas R. Anderson.

51

Variational problems over time scales

VERA ZEIDAN

Michigan State University


East Lansing, Michigan, USA

[email protected]

http://www.math.msu.edu/˜zeidan

This talk focuses on the study of variational problems over time scale which encompassesboth nonlinear optimal control and calculus of variations problems. The main goal is centeredon the question of deriving necessary and sufficient optimality criteria of first and second order.The special feature resides in the fact that these conditions are formulated in terms of a certain“Hamiltonian” corresponding to the nonlinear problem. The second order conditions are ob-tained in terms of the accessory problem. However, Reid roundabout theorems, that are recentlyobtained with R. Hilscher, allow these conditions to be equivalently phrased in terms of conjoinedbasis and Riccati equations corresponding to the accessory problem.

52

Abstracts of Contributed Talks

53

General solution of linear homogeneous difference

equations with variable coefficients

JESUS ABDERRAMAN

Universidad Politecnica de Madrid, Campus Montegancedo

Department of Applied Mathematics, Faculty of Computer Science

Madrid, Spain

[email protected]

http://www.dma.fi.upm.es/jesus

A constructive theory for the general solution of kth-order difference equation

x(k)(n+ 1) =k−1∑i=0

pi+1(n)x(k)(n− i)

is given as in a forthcoming paper of the author. As complement of the analytical theory [GeorgeD. Birkhoff, General theory of linear difference equations, Transactions of the American Mathe-matical Society, volume 12, number 2, pages 243–284, 1911], this constructive approach permitsus an explicit and nonrecurrent representation of the general solution, for any initial conditions,x−1, x0, . . . , xk−2, and any sequences of complex numbers, pi+1(j)n−1

j=k−2, i = 0, . . . , k − 1. Ifk = 1, then the solution is straightforward. For k > 1, a simple change of variable produces anequivalent kth-order linear difference equation that permits us to solve x(k)(n), n ≥ k − 1, byinduction on n. Since the representation for the general case is too long, the solution for k = 2 isprovided here as an illustration:

x(2)(n) =n−1∏i=0

p1(i)(c0Φ(2,0)

n (α2(1), . . . , α2(n− 1)) + c−1α2(0)Φ(2,1)n−1 (α2(2), . . . , α2(n− 1))

),

where c−1, c0 are arbitrary numbers, n ≥ 1, j = 0, 1, α2(k) = p2(k)p1(k−1)p1(k) , α2(0) = p2(0)

p1(0). Φ(2,j)

n−j (~α)are:

Φ(2,j)n−j (~α) =

bn−j2 c∑

l=0

n−1∑k1=2l−1+j

α2(k1)

k1−2∑k2=2(l−1)−1+j

α2(k2)

· · ·kl−1−2∑

kl=1+j

α2(kl)

.

When l = 0, the sum is 1 by convention.

AMS Subject Classification: 39A05.Keywords: Linear difference equations.

54

Periodicity in nonlinear

systems of dynamic equations

MURAT ADIVAR

Izmir University of Economics

Izmir, Turkey

[email protected]

http://homes.ieu.edu.tr/˜madivar

By means of Schaefer’s fixed point theorem, we show the existence of periodic solutions ofa nonlinear system of Volterra-type integro-dynamic equations. Furthermore, we provide severalapplications to scalar equations, where we develop a time scale analogue of Lyapunov’s directmethod and prove an analogue of Sobolev’s inequality on time scales to arrive at a priori boundon all periodic solutions.

AMS Subject Classification: 39A10.Keywords: Time Scale, dynamic equation, fixed point theorems.This is joint work with Youssef Raffoul.

55

A new method for solving

fuzzy partial differential equations

MOZHDEH AFSHAR KERMANI

Islamic Azad University North Tehran Branch


Tehran, Iran

mog [email protected]

In this talk a new method for solving “fuzzy partial differential equations” (FPDE) is consid-ered. This numerical method based on the definition of derivative that considered by Y. Chalco-Cano, H. Roman-Flores. We present a difference method to solve FPDEs such as the fuzzy hyper-bolic equation and fuzzy parabolic equation, then see if stability of this method exist, and condi-tions for stability are given. Examples are presented showing the Hausdorff distance between theexact solution and approximate solution is small.

Keywords: Fuzzy partial differential equation, difference method.

56

Using B-spline scaling functions

for solving integro-differential equations

NASSER AGHAZADEH

Azarbaijan University of Tarbiat Moallem


Tabriz, Iran

[email protected]

http://www.azaruniv.edu/˜aghazadeh

In this talk, quadratic semiorthogonal B-spline scaling functions together with their dualfunctions are developed to approximate the solutions of linear second-order Fredholm integro-differential equations. The quadratic B-spline scaling functions, their properties and the opera-tional matrices of derivative for B-spline scaling functions are presented and are utilized to reducethe solution of Fredholm integro-differential to the solution of algebraic equations. The methodis computationally attractive, some numerical examples are presented to support our work.

AMS Subject Classification: 45B05, 45A05, 65D07, 42C05.Keywords: Quadratic spline, Fredholm integro-differential equation.

57

A trace formula for an

abstract Sturm–Liouville operator

INCI ALBAYRAK

Yıldız Technical University

Mathematical Engineering Department

Istanbul, Turkey

[email protected]

http://www.mtm.yildiz.edu.tr/cvler/ialbayrak

In this talk we investigate and obtain a regularized trace formula for the operator in theHilbert space L2([0, 1],H) generated by the expression

−y′′(x) +Q(x)y(x)

with the boundary conditions

y(0) = 0, y′(1) +Ay(1) = 0,

where H is a separable Hilbert space, for x ∈ [0, 1], Q(x) is a self-adjoint nuclear operator definedin H , and A is a real number.

This is joint work with Kevser Koklu and Azad Bayramov

58

Periodic and eventually periodic orbits

for skew-product maps

DIANA ALDEA MENDES

IBS-ISCTE Business School, ISCTE

Department of Quantitative Methods

Lisbon, Portugal

[email protected]

http://iscte.pt/˜deam

In this talk we consider triangular (or skew-product) maps of the real plane that admit peri-odic and eventually periodic critical orbits. A corresponding Markov partition will be constructedfor these maps. We also show that there exist an invariant probability measures, namely the Parrymeasure. In order to obtain these, we apply some tensor products between the invariants associ-ated with the one-dimensional components of the triangular map. An immediate consequence isthe computation of the topological and metric entropy for these maps.

AMS Subject Classification: Primary 37B10, 37B40, 37E30; Secondary 15A69.Keywords: Skew product, periodic orbits, Markov partition.

59

The effect of harvesting strategies on

the discrete Beverton–Holt model

ZIYAD AL-SHARAWI

Sultan Qaboos University


Al-Khod, Muscat, Oman

[email protected]

We discuss the effect of constant, periodic and conditional harvesting strategies on the dis-crete Beverton–Holt model. We find that for large initial populations, constant harvesting givesthe maximum sustainable yield. Periodic harvesting has a short term advantage when the initialpopulation is small, and conditional harvest has the advantage of lowering the risk of extinction.Also, we discuss the periodic character in each case, and show that periodic harvesting drivespopulation cycles to be multiples (period wise) of the harvesting period.

AMS Subject Classification: 39A11, 92D25, 92B99.Keywords: Beverton–Holt model, optimal harvesting.This is joint work with Mohamed Rhouma.

60

Asymptotic behavior of linear

impulsive delay difference equations

JEHAD ALZABUT

Cankaya University

Department of Mathematics and Computer Science

Ankara, Turkey

[email protected]

http://math.cankaya.edu.tr/˜jehad

In this talk, it is shown that if a linear impulsive delay difference equation satisfies Perron’scondition, then its trivial solution is asymptotically stable.

AMS Subject Classification: 39A13, 34K45.Keywords: Impulse, delay, adjoint, Perron, stability.This is joint work with Thabet Abdeljawad.

61

Growth, long memory and heavy tails in difference

equation models of inefficient financial markets

JOHN APPLEBY

Dublin City University

School of Mathematical Sciences

Dublin, Ireland

[email protected]

http://webpages.dcu.ie/˜applebyj

In this talk we explore the asymptotic behaviour of a stochastic difference equation modelof a financial market in which traders use the past behaviour of prices to guide their investmentdecisions.

For a class of affine and maximum type functional difference equations we find an exactexponential rate of growth, just as is seen in classical efficient market models. We also show thatthese models possess the property of “long memory” in that the autocovariance function of thereturns decays so slowly that it is nonintegrable. Furthermore, the asset returns are seen to exhibit“heavy tails”, in that the distribution function of the returns decay polynomially.

All the results will be shown to be dynamically consistent with corresponding continuous-time functional differential equation models. The work is joint with Huizhong Wu and CatherineSwords and is supported by the SFI RFP Grant 05/MAT/0018 “Stochastic Functional DifferentialEquations with Long Memory”.

Keywords: Stochastic difference equation, long memory.This is joint work with Catherine Swords and Huizhong Wu.

62

Asymptotic formulas for Laplace integrals

SAMAR ASEERI

Umm Al-Qura University


Makkah, Saudi Arabia

[email protected]

Solutions of boundary value problems of mathematical physics often involve infinite inte-grals containing a term consisting of a trigonometrical or Bessel function, with the aid of Laplaceintegral transform, as an integral equation of the first kind, the solution of the integral equation isobtained. In this talk, many applications on this manner are discussed and solved.

AMS Subject Classification: 65R10.Keywords: Laplace transforms, boundary value problems.

63

On a class of rational difference equations

NURIYE ATASEVER

Selcuk University

Department of Mathematics, Education Faculty

Konya, Turkey

atasever [email protected]

In this talk we study the behaviour of the positive solutions of the nonlinear difference equa-tion

xn+1 = ((xn−k)/(1 + xn−1xn−3 . . . xn−(k−2))), n = 0, 1, 2, . . . ,

where k > 2 is an odd integer.

AMS Subject Classification: 39A10.Keywords: Difference equation, positive solutions.This is joint work with Cengiz Cinar, Dagıstan Simsek, and Ibrahim Yalcınkaya.

64

Stability of coupled difference equations with delays

FATIHCAN M. ATAY

Max Planck Institute

Mathematics in the Sciences

Leipzig, Germany

[email protected]

http://personal-homepages.mis.mpg.de/fatay

Networks of diffusively-coupled scalar maps are considered with weighted connections whichmay include a time delay. The stability of equilibria is studied with respect to the delays and con-nection structure. It is shown that the largest eigenvalue of the graph Laplacian determines theeffect of the connection topology on stability. The stability region in the parameter plane shrinkswith increasing values of the largest eigenvalue, or of the time delay of the same parity. In partic-ular, all bipartite graphs have an identical stability region, regardless of the delay or graph size,which is also the smallest stability region among those of all graphs. Furthermore, for certainparameter ranges, unstable (and possibly chaotic) maps can be stabilized via diffusive couplingwith an odd time delay, provided that the network does not have a nontrivial and connected bi-partite component. On the other hand, stabilization is not possible for even values of the delay orfor bipartite networks.

Reference: F. M. Atay and O. Karabacak. Stability of coupled map networks with delays.SIAM Journal on Applied Dynamical Systems, 5:508–527, 2006.

AMS Subject Classification: 39A11, 37E05, 94C15.Keywords: Network, delay, stability, synchronization, chaos, Laplacian.

65

Initial value problems in discrete fractional calculus

FERHAN ATICI

Western Kentucky University


Bowling Green, Kentucky, USA

[email protected]

http://www.wku.edu/˜ferhan.atici

This paper is devoted to the study of discrete fractional calculus; the particular goal is todefine and solve well-defined discrete fractional difference equations. For this purpose we firstcarefully develop the commutativity properties of the fractional sum and the fractional differenceoperators. Then a ν-th (0 < ν ≤ 1) order fractional difference equation is defined. A nonlinearproblem with an initial condition is solved and the corresponding linear problem with constantcoefficients is solved as an example. Further, the half-order linear problem with constant coef-ficients is solved with a method of undetermined coefficients and with a transform method.

AMS Subject Classification: 39A12, 34A25, 26A33.Keywords: Discrete fractional calculus.This is joint work with Paul Eloe.

66

Constructing difference equations models

for public health policy

TAMARA AWERBUCH FRIEDLANDER

Harvard School of Public Health

Department of Global Health and Population

Boston, Massachusetts, USA

[email protected]

http://www.hsph.harvard.edu/research/

→tamara-awerbuchfriedlander

Difference equations modeling exploits the natural connection between events occurring atdiscrete intervals and the inherent discrete nature of difference equations. We will show exam-ples used for understanding complex interactions among ecological components that lead to thespread of diseases transmitted by vectors such as ticks and mosquitoes. The emergence of Lymedisease and its early stages was represented and analyzed as a linear system; the system repre-senting later stages of the tick population growth rendered a delay equation with two parameterswhich are real numbers representing biological characteristics of the tick life-cycle. The mathe-matical analysis enables us to detect parameter regions of local and global stability, boundednessand oscillatory behavior of solutions. Another example is the construction of nonlinear systemsdescribing community intervention in mosquito control through management of their habitats.One system consists of two equations; representing a more complex intervention resulted in asystem of three difference equations. The work has been carried out by a collaboration of aninterdisciplinary team of mathematicians, biologists, ecologist, sociologists.

Keywords: System, difference equations, infectious diseases.

67

Fredholm integral equations on time scales

OZLEM BATIT

Ege University


Izmir, Turkey

[email protected]

http://sci.ege.edu.tr/˜math/index.php?

→option=com content&task=view&id=55

In this talk, we study linear and nonlinear Fredholm integral equations on time scales. Firstseparable kernels and then symmetric kernels are considered for the linear case. For the nonlinearcase, we use the monotone iterative technique to obtain approximations to a unique solution andgive some applications.

AMS Subject Classification: 45B05.Keywords: Time scales, Fredholm integral equations.

68

A Sharkovsky theorem for maps on trees

CHRIS BERNHARDT

Fairfield University


Fairfield, Connecticut, USA

[email protected]

http://cs.fairfield.edu/˜bernhardt

The proof of Sharkovsky’s theorem is combinatorial in nature. This means that instead ofviewing it as a theorem about maps of the interval one can view it as a theorem about maps ontrees that permute the vertices in the special case when the tree is topologically an interval. Thisway of viewing Sharkovsky’s theorem leads to the natural question of whether there is such atheorem for trees in general.

In this talk we give a Sharkovsky-type ordering for trees in general. We also show the con-verse — that given any n there is a tree and a map that has exactly the periods given by thetheorem.

69

Exponentially asymptotically constant systems

of difference equations with applications

SIGRUN BODINE

University of Puget Sound


Tacoma, Washington, USA

[email protected]

We consider the asymptotic behavior of solutions of systems of linear difference equationsof the form

y(n+ 1) = [A+R(n)] y(n) , n ≥ n0,

where A is a constant, invertible matrix and R(n) is an exponentially small perturbation, i.e.,|R(n)| ≤ Kεn for some 0 < ε < 1. While classical results yield, for n sufficiently large, theexistence of a fundamental matrix of the form

Y (n) = [I + o(1)]An as n→∞,

we want to find more precise estimates of the error term o(1). In particular, we are interested inits dependence on ε and the eigenvalues of A.

We also present an application to nonlinear autonomous dynamical systems with hyperbolicequilibria.

Our results were motivated by a recent paper by R. Agarwal and M. Pituk who studied scalarlinear difference equations with exponentially small perturbations.

AMS Subject Classification: 39A11.Keywords: Exponentially small perturbations, asymptotics.This is joint work with D. A. Lutz.

70

Necessary and sufficient conditions for oscillation

of certain higher order partial difference equations

YASAR BOLAT

Afyon Kocatepe University


Afyonkarahisar, Turkey

[email protected]

http://www2.aku.edu.tr/˜yasarbolat

In this talk, some necessary and sufficient conditions for the oscillation of a certain higherorder partial difference equation are obtained.

AMS Subject Classification: 39A11, 34K11, 34C10.Keywords: Partial difference equation, oscillation, oscillatory.This is joint work with Omer Akın.

71

On the equivalence of Rolle’s and generalized

mean value theorems on time scales

DEVRIM CAKMAK

Gazi University

Department of Mathematics Education

Ankara, Turkey

[email protected]

http://websitem.gazi.edu.tr/dcakmak

In this talk, by using elementary time scale calculus, we recall the equivalence between well-known Rolle’s and Generalized Mean Value Theorems on time scales.

AMS Subject Classification: 26A24, 39A12.Keywords: Rolle’s theorem, mean value theorem, time scales.

72

On the global character of solutions of a

rational system of difference equations

ELIAS CAMOUZIS

American College of Greece

Department of Mathematics and Natural Sciences

Athens, Greece

[email protected]

In this talk we study the global character of solutions of a rational system of difference equa-tions. In particular, we examine the boundedness of solutions, the stability of the equilibriumpoints, and the periodic character of solutions.

AMS Subject Classification: 39A10.Keywords: Rational system, boundedness, stability, periodicity.

73

A characterization of k-cycles

JOSE S. CANOVAS

Technical University of Cartagena

Department of Applied Mathematics and Statistics

Cartagena, Spain

[email protected]

http://filemon.upct.es/˜jose

We study global periodicity for the difference equation of order l given by

xn+l = f(xn+l−1, xn+l−2, . . . , xn),

where f : (0,∞)l → (0,∞) is a continuous map, l ∈ Z+. Our main results are the following. Weprove that if any solution of the equation is periodic, then there is a minimal k ∈ N such that theperiod of any solution divides k (and therefore f is called a k-cycle). In addition, if l = 2, then forany k > 2 there are, up to conjugacy, only a k-cycle. Finally, if l > 2 and f gives a (l + 1)-cycle,then f is conjugated to:

• xn+l = 1xn·xn+1·...·xn+l−1

, if l is even.

• The previous equation or xn+l =

(l+1)/2Qj=1

xn+2j−2

(l−1)/2Qj=1

xn+2j−1

, if l is odd.

AMS Subject Classification: 39A05.Keywords: Cycles, conjugacy.This is joint work with Antonio Linero and Gabriel Soler.

74

Higher-order boundary value problems on time scales

ERBIL CETIN

Ege University


Izmir, Turkey

[email protected]


→option=co m content&task=view&id=63

In this talk, we give the existence of positive solutions of the Lidstone boundary value prob-lem (LBVP) (−1)ny4

2n

(t) = f(t, yσ(t)), t ∈ [0, 1],

y42i

(0) = y42i

(σ(1)) = 0, 0 ≤ i ≤ n− 1,

where n ≥ 1 and f : [0, σ(1)]× R → R is continuous.

Firstly, by using the Schauder fixed point theorem in a cone, we obtain the existence of solu-tions to a Lidstone boundary value problem (LBVP). Secondly, an existence result for this problemis also given by the monotone method. Finally, by using the Krasnosel’skii fixed point theorem, itis proved that the LBVP has a positive solution.

AMS Subject Classification: 39A10.Keywords: Positive solutions, upper and lower solutions.This is joint work with Fatma Serap Topal.

75

Effect of floating point on computation

of monodromy matrix

ALI OSMAN CIBIKDIKEN

Selcuk University

Department of Computer Technology and Programming

Konya, Turkey

[email protected]

asp.selcuk.edu.tr/asp/personel/

→web/goster.asp?sicil=5377

LetA(n) be a matrix of dimensionN×N with period T and consider the difference equationsystem

x(n+ 1) = A(n)x(n), n ∈ Z. (1)

With X(T ) being the monodromy matrix of the system (1), it is well known that

ω1(A, T ) =

∣∣∣∣∣∣∣∣∣∣∞∑

k=0

(X∗(T ))k(X(T ))k

∣∣∣∣∣∣∣∣∣∣ <∞ (2)

implies Schur stability of the system (1) [Kemal Aydın, A. Ya. Bulgakov, Gennadii Demidenko,Numerical characteristics of asymptotic stability of solutions of linear difference equations withperiodic coefficients, Siberian Mathematical Journal, volume 41, number 6, pages 1005–1014,2000]. By the spectral criterion, each eigenvalue of the monodromy matrix X(T ) belongs to theunit disk [Saber Elaydi, An introduction to difference equations, third edition, undergraduatetexts in mathematics, Springer, New York, 2005]. Schur stability of the system (1) depends on themonodromy matrix X(T ) in both cases. Therefore, Schur stability of the system (1) and quality ofSchur stability are related to the results of computation errors on computation of the monodromymatrix X(T ). In this study, the effect of floating point on computation of the monodromy matrixX(T ) is investigated. The bound is obtained for ||X(T )− Y (T )|| in which the matrix Y (T ) is thecomputed value of the monodromy matrix.

AMS Subject Classification: 39A11, 65G50.Keywords: Schur stability, monodromy matrix, roundoff error.This is joint work with Kemal Aydın.

76

Study of attractors for two-dimensional

skew-products whose basis

is a Denjoy counterexample

SARA COSTA



Bellaterra (Cerdanyola del Valles), Spain

[email protected]

Since Keller studied, in 1996, the existence of strange nonchaotic attractors in a particularkind of two-dimensional quasiperiodically forced skew-products defined on M+ := S1 × [0,∞),several extensions of his results have been published. All these extensions have in common thatthe system are defined on M+, and the component on the basis is always an irrational rotation.We extend the Keller and Haro results to similar systems defined on S1 × R, in this case we canhave two attractors given by the graph of a map defined on S1 or only one given by the graph of atwo-valued correspondence. If we exchange the irrational rotation by a Denjoy counterexample,the results are quite similar with the difference that the map, or correspondence, whose graphgives the attractor is defined on P ⊂ S1, where P is the support of the unique invariant measureof the Denjoy counterexample.

This is joint work with Lluıs Alseda.

77

Difference equations arising in dynamic

models of biological evolution

J. M. CUSHING

University of Arizona


Tucson, Arizona, USA

[email protected]

http://math.arizona.edu/˜cushing

I will describe some nonlinear difference equation models that arise in modeling the evolu-tion of biological populations. The state variables are mean phenotypic traits of species as well asthe usual population densities, and consequently the models involve systems of (or higher order)nonlinear difference equations. The models typically have several equilibria and a fundamentalquestion concerns which are stable. I will give some stability results and some open problemsand conjectures.

AMS Subject Classification: 37N25, 92D25.Keywords: Difference equations, models of evolution.

78

A new proof for the Levin–May

criterion of asymptotic stability

FOZI DANNAN

Arab International University


Damascus, Syria

[email protected]

Levin and May obtaind an easy necessary and sufficient condition for the asymptotic stabil-ity of the difference equation x(n+ 1)− x(n) + qx(n− k) = 0. In this talk we give a new proof forthis condition.

AMS Subject Classification: 39A11.Keywords: Levin–May, asymptotic stability, difference equation.

79

On nonoscillation of

Emden–Fowler difference equations

ZUZANA DOSLA

Masaryk University



[email protected]

http://www.math.muni.cz/˜dosla

Asymptotic properties of nonoscillatory solutions of the Emden–Fowler equation

∆(an|∆xn|αsgn ∆xn) + bn|xn+1|β sgn xn+1 = 0, α 6= β, (1)

are investigated using the half-linearization technique.

Some interesting discrepancies concerning oscillation and nonoscillation of (1) and its con-tinuous counterpart will be given.

This is joint work with Mariella Cecchi and Mauro Marini.

80

Sensitivity of Schur stable linear systems

with periodic coefficients

AHMET DUMAN




[email protected]

http://www.akademi.aku.edu.tr/

→frmCvler.aspx?SicilNo=KA0992

Let A(n) be an N ×N -matrix with period T and consider the difference equation system

x(n+ 1) = A(n)x(n), n ∈ Z. (1)

With X(T ) being the monodromy matrix of (1), it is well known that

w1(A, T ) =

∣∣∣∣∣∣∣∣∣∣∞∑

k=0

(X∗(T ))k (X(T ))k

∣∣∣∣∣∣∣∣∣∣ <∞

implies Schur stability of the system (1) [Kemal Aydın, A. Ya. Bulgakov, Gennadii Demidenko,Numerical characteristics of asymptotic stability of solutions of linear difference equations withperiodic coefficients, Siberian Mathematical Journal, volume 41, number 6, pages 1005–1014,2000]. Let B(n) be a matrix of dimension N × N with period T . There are some results givenon the Schur stability of the perturbated system

y(n+ 1) = [A(n) +B(n)]y(n), n ∈ Z, (2)

whereB(n) is the perturbation matrix [Kemal Aydın, Haydar Bulgak, Gennadii Demidenko, Con-tinuity of numeric characteristics for asymptotic stability of solutions to linear difference equa-tions with periodic coefficients, Selcuk Journal of Applied Mathematics, volume 2, number 2,pages 5–10, 2001]. Note: Haydar Bulgak is the same person as A. Ya. Bulgakov.

In this talk, we give new results for Schur stability of the system (2) and compare thesenew results with the existing ones in the literature. The results are supported with numericalapplications too.

AMS Subject Classification: 39A11.Keywords: Schur stability, monodromy matrix, sensitivity.This is joint work with Kemal Aydın.

81

Comparison and oscillation theorems for linear and

half-linear dynamic equations on time scales

LYNN ERBE

University of Nebraska–Lincoln



[email protected]

http://www.math.unl.edu/˜lerbe2

We obtain some new oscillation and comparison results for the second-order linear (or half-linear) dynamic equation of the form (r(x∆)α)∆(t)+p(t)xα(σ(t)) = 0. We are primarily interestedin the case when the coefficient p(t) changes sign for arbitrarily large values of t. The resultsimprove and extend some earlier criteria, in both the continuous and discrete cases, as well as formore general time scales.

AMS Subject Classification: 34K11, 39A10.Keywords: Comparison theorems, oscillation, half-linear.This is joint work with Jia Baoguo and Allan Peterson.

82

The structure of the spectrum for normal operators

MELTEM EROL

Karadeniz Technical University


Trabzon, Turkey

[email protected]

We have investigated the structure of the spectrum for normal operators on a Hilbert spacewith a new method and asymptotic behavior of its eigenvalues. The obtained results in thiswork can be applied to a normal extension of minimal operators generated by a linear differentialoperator expression in a Hilbert space of vector functions in finite intervals.

AMS Subject Classification: 47A10.Keywords: Normal operators, spectrum.This is joint work with Zameddin Ismailov.

83

Convergence of hyperspaces under the Fell topology,

especially of time scales

NORAH ESTY

Stonehill College


Boston, Massachusetts, USA

[email protected]

In this talk we will examine various topologies on hyperspaces, and in particular those whichare most useful in the context of time scales. After demonstrating that the Fell topology is the mostappropriate, we will state (and time permitting, prove) several theorems about convergence inhyperspaces of locally compact metric spaces under the Fell topology. Finally we will state/proveanalogous theorems for the particular case of time scales, where the hyperspace in questions isCL(R).

AMS Subject Classification: 54B20.Keywords: Hyperspaces, time scales, Fell topology.This is joint work with Stefan Hilger.

84

Systoles and topological entropy

in discrete dynamical systems

SARA FERNANDES

Universidade de Evora / CIMA-UE

Research Centre in Mathematics and Application

Evora, Portugal

[email protected]

http://evunix.uevora.pt/˜saf

The fruitful relationship between the geometry and the graph theory has been explored byseveral authors in the sense of bringing important results for the discrete dynamical systems seenas Markov chains in graphs. In this work we will explore the relationship between the topologicalentropy and systoles in the context of maps on the interval.

AMS Subject Classification: 37A35, 37B10.Keywords: Dynamical systems, topological entropy, systole.This is joint work with Clara Gracio and Carlos Ramos.

85

Optimal monetary policy with

partially rational agents

ORLANDO GOMES

Instituto Politecnico de Lisboa, UNIDE/ISCTE

Escola Superior de Comunicacao Social

Lisbon, Portugal

[email protected]

We explore the dynamic behavior of a New Keynesian monetary policy problem with expec-tations formed, partially, under adaptive learning. We consider two alternative cases: on the firstsetting, the private economy has the ability to predict rationally real economic conditions (theoutput gap) but it needs to learn about the future values of the nominal variable (the inflationrate); on the second setup, private agents are fully aware of future inflation rates, however theylack the ability to predict instantly the correct values of the output gap (learning is attached to thisvariable). In both cases, we find a simple condition indicating the required learning quality thatis needed to guarantee local stability. To achieve convergence to the steady state, the economydoes not need to attain full learning efficiency; it just has to secure a minimum learning quality inorder to attain the desired long run result.

Keywords: Optimal monetary policy, adaptive learning.This is joint work with Vivaldo M. Mendes and Diana A. Mendes.

86

Stability boundary for asymptotic stability

of scalar equations

OZLEM AK GUMUS

Selcuk University

Department of Mathematics, Faculty of Science and Literature

Konya, Turkey

[email protected]

http://asp.selcuk.edu.tr/asp/personel/web/

→goster.asp?sicil=6644

We consider the scalar equation of the form

x(n+ 2k) + px(n+ k) + qx(n) = 0

and obtain stability regions in the plane by using the Schur–Cohn criterion. In the case of p = 1 orp = −1, the obtained stability region is restricted to a narrow area by the found values of q whenk is a positive even integer.

Keywords: Stability, discrete-time system, stability criteria.This is joint work with Necati Taskara.

87

Spectral analysis of a non-selfadjoint

second-order difference operator

GUSEIN GUSEINOV

Atılım University


Ankara, Turkey

[email protected]

http://www.atilim.edu.tr/˜guseinov

Non-Hermitian (non-selfadjoint) Hamiltonians and complex extension of quantum mechan-ics have recently received a lot of attention [C. M. Bender, Making sense of non-Hermitian Hamil-tonians, Rep. Progr. Phys. 70(2007), 947–1018]. In this study, we develop spectral analysis of thediscrete problem

−∆2yn−1 + qnyn = λρnyn, n ∈ . . . ,−3,−2,−1 ∪ 2, 3, 4, . . ., (1)

y−1 = y1, ∆y−1 = e2iδ∆y1, (2)

in the Hilbert space l2, where (yn), n ∈ Z = 0,±1,±2,±3, . . ., is a desired solution, ∆ denotesthe forward difference operator defined by ∆yn = yn+1−yn (so that ∆2yn−1 = yn−1−2yn +yn+1),qn ≥ 0, λ is a spectral parameter, and

ρn =

e2iδ, n ≤ −1,e−2iδ, n ≥ 0,

(3)

for a δ ∈ [0, π/2). The main distinguishing features of problem (1), (2) are that it involves acomplex coefficient ρn of the form (3) and that transition conditions (impulse conditions) of theform (2) are presented which also involve a complex coefficient. Such a problem is not self adjointwith respect to the usual inner product of space l2 and it arises as a discrete version of somequantum systems on a complex contour.

AMS Subject Classification: 39A70.Keywords: Difference operator, spectrum, completely continuous operator.This is joint work with Ebru Ergun.

88

Interval oscillation of second-order difference

equations with oscillatory potentials

A. FEZA GUVENILIR

Ankara University


Ankara, Turkey

[email protected]

Interval oscillation criteria are established for second-order difference equations of the form

∆(k(n)∆x(n)) + p(n)x(g(n)) + q(n)|x(g(n))|α−1x(g(n)) = e(n),

where n ≥ n0, n0 ∈ N = 0, 1, . . ., α > 1; k(n), p(n), q(n), g(n), and e(n) are sequencesof positive real numbers, k(n) > 0 is nondecreasing, g(n) is nondecreasing with g(n) → ∞ asn→∞, ∆ is the forward difference operator defined as usual by ∆x(n) = x(n+ 1)− x(n).

AMS Subject Classification: 34K11, 34C15.Keywords: Interval oscillation, second order, delay argument.

89

Discrete Haavelmo growth cycle model

MAŁGORZATA GUZOWSKA

University of Szczecin

Department of Econometrics and Statistics

Szczecin, Poland

[email protected]

A discretization method attributed to Kahan is used to approximate the Haavelmo growthcycle model. The local dynamics of this discrete-time Haavelmo growth cycle model are analyzed.

Keywords: Kahan’s method, discrete time, Haavelmo model.

90

Solving systems of nonlinear equations

by using difference equations

MOGHTADA HASHEMIPARAST

K. N. T. University of Technology


Tehran, Iran

[email protected]

http://www.math.kntu.ac.ir/hashemiparast.htm

There are many numerical methods in obtaining the solution of integral equations, system ofintegral equations or integro-differential equations which reduce to a system of nonlinear equa-tions. These problems are often ill posed, and are difficult to be solved. In this talk, by usinga moment characteristic function, these systems are transferred to a set of difference equations.The solution is obtained, by referring to the applied characteristic function. Finally, numericalexamples are given.

Keywords: Characteristic function, difference equation.

91

The dynamic multiplier-accelerator

model in economics

JULIUS HEIM




[email protected]

http://math.mst.edu

In this work we derive a linear second-order dynamic equation which describes multiplier-accelerator models in economics on time scales. After we provide the general form of the dy-namic equation, which considers both taxes and foreign trade, i.e., imports and exports, we givefour special cases of this general multiplier-accelerator model: (1) Samuelson’s basic multiplier-accelerator model. (2) We extend this model with the assumption that taxes are raised by the gov-ernment and that these taxes are immediately reinvested by the government. (3) We give Hicks’extension of the basic multiplier-accelerator model as an example and (4) extend this model byallowing foreign trade in the next step. For each of these models we present the dynamic equationin both expanded and self-adjoint form and give examples for particular time scales. Finally wepresent a criterion under which each solution of the dynamic equation oscillates.

AMS Subject Classification: 91B62, 34C10, 39A10, 39A11, 39A12, 39A13.Keywords: Time scales, multiplier-accelerator, dynamic equation, self adjoint, economics.This is joint work with Martin Bohner.

92

Riccati equations for linear Hamiltonian systems

ROMAN HILSCHER

Masaryk University



[email protected]

http://www.math.muni.cz/˜hilscher

In this talk we will discuss Riccati matrix differential and difference equations for (possiblyabnormal) linear Hamiltonian and symplectic systems. The abormality is reflected in the (possi-ble) noninvertibility of the corresponding principal solution. We show that even in this case onecan characterize the nonnegativity and positivity of the associated quadratic functional via certainimplicit Riccati equations. These results are derived through the general time scales theory andextend the known classical continuous time results e.g., by Reid and Coppel and recent discretetime results e.g., by Bohner, Dosly, Kratz, and Ruzickova.

AMS Subject Classification: 34C10, 39A12.Keywords: Time scale, Riccati equation, generalized inverse.This is joint work with Vera Zeidan.

93

On the global stability of xn+1 = p+qxn1+xn−1

V ICTOR JIMENEZ LOPEZ

Universidad de Murcia

Departamento de Matematicas

Murcia, Spain

[email protected]

http://www.um.es/docencia/vjimenez

For a long time it has been conjectured that the unique positive equilibrium of the equationfrom the title attracts all its positive solutions. The conjecture is known to be true in the casesq < 1 (Kulenovic and Ladas, 2001) and p ≤ q (Kocic and Ladas, 1993). Under the assumptionsq ≥ 1 and q < p it has been proved in progressively more general settings by Kocic, Ladas andRodrigues (1993), Ou Tang and Luo (2000) and Nussbaum (2007). A paper by Li, Zhang and Su(2005) purportedly provides a full proof of the conjecture but in fact has a rather basic mistake.

In this work we use a modified version of the so-called dominance condition, a tool recentlyintroduced by H. El-Morshedy and the author (“Global attractors for difference equations dom-inated by one-dimensional maps”, J. Difference Equ. Appl. 14 (2008), 391–410) to give a unifiedproof on the conjecture in the cases listed above and improve Nussbaum’s bounds.

AMS Subject Classification: 39A11, 37C70.Keywords: Global attractor, rational difference equation.

94

Period-two trichotomies of a difference equation

of order higher than two

SENADA KALABUSIC

University of Sarajevo

Department of Mathematics, Faculty of Science

Sarajevo, Bosnia and Herzegovina

[email protected]

http://www.pmf.unsa.ba

We investigate the period-two trichotomies of solution of the equation

xn+1 = f(xn, xn−1, xn−2), n = 0, 1 . . . ,

where the function f satisfies certain monotonicity conditions. We give fairly general conditionsfor period-two trichotomies to occur and illustrate the results with numerous examples.

AMS Subject Classification: 39A10, 39A11.Keywords: Attractivity, period two solution, unbounded.This is joint work with Dz. Burgic and M. R. S. Kulenovic.

95

Iterated oscillation criteria for delay

dynamic equations of first order

BASAK KARPUZ


Department Mathematics


[email protected]

http://www.akademi.aku.edu.tr/

→frmCvler.aspx?SicilNo=KA1798

We obtain new sufficient conditions for the oscillation of all solutions of first-order delaydynamic equations on arbitrary time scales, hence combining and extending results for corre-sponding differential and difference equations.

AMS Subject Classification: 39A10, 34C10.Keywords: Oscillation, first-order delay dynamic equations.This is joint work with Martin Bohner and Ozkan Ocalan.

96

Dynamic equations with

piecewise continuous argument

CHRISTIAN KELLER




[email protected]

We extend the theory of differential equations with piecewise continuous argument to gen-eral time scales. Systems with alternating retarded and advanced argument will be investigatedand conditions for globally asymptotic stability of those systems will be stated. Furthermore westudy the oscillatory behaviour for several dynamic equations with piecewise continuous argu-ment.

AMS Subject Classification: 34K11, 39A10, 39A11, 39A12, 39A13.Keywords: Dynamic equation, time scale, piecewise continuous, retarded, advanced, delay.This is joint work with Martin Bohner.

97

A cardiac loop reentry model with thresholds

CANDACE KENT

Virginia Commonwealth University

Department of Mathematics and Applied Mathematics

Richmond, Virginia, USA

[email protected]

http://www.math.vcu.edu/faculty/kent.html

We investigate the two-dimensional, multiple threshold map, or bimodal system,

F (x , y) =

G(x , y) , if (x , y) ∈ TH(x , y) , if (x , y) /∈ T ,

where G : R2+ → R2

+ and H : R2+ → R2

+ are continuous and T is the intersection of five thresholdregions. Sufficient conditions are placed on G and H that guarantee that either every orbit underF that begins in T leaves T and never returns or there exist orbits under F that begin in T andpass between T and its complement infinitely often. Our bimodal system is intended to serve asa simple discrete model of the dynamics of a circulating pulse of depolarization in a ring of twocardiac cells within the context of cardiac arrhythmias or irregular heartbeat.

This is joint work with Hassan Sedaghat.

98

Asymptotic behavior of one class solutions of the

second-order Emden–Fowler difference equation

VITALIY KHARKOV

I. I. Mechnikov Odessa National University


Odessa, Ukraine

kharkov v [email protected]

In this talk we investigate and obtain necessary and sufficient conditions for existence ofone nontrivial class solutions of the second-order Emden–Fowler difference equation. Moreover,asymptotic representations of solutions from this class are established.

AMS Subject Classification: 34D05.Keywords: Asymptotics, Emden–Fowler equation.

99

Stability via Convexity

MIKHAIL KIPNIS

Chelyabinsk State Pedagogical University


Chelyabinsk, Russia

[email protected]

Stability analysis of the Volterra difference equations

xn +n∑

m=1

amxn−m = 0, n = 1, 2 . . . (1)

is presented, with assumption that the series∑∞

m=1 am is convergent, and inequalities am ≥ 0and ∆2am = am − 2am+1 + am+2 ≥ 0 hold for all m ∈ N. For example, let am = β/ms for real βand s > 1. The criterion for asymptotic stability of equation (1) is given by

− 1ζ(s)

= − 1∑∞m=1

1ms

< β <1∑∞

m=1(−1)m+1 1ms

=1

(1− 21−s) ζ(s),

where ζ(s) is Riemann’s zeta function. Results obtained for the difference equations of the k-thorder were compared with the Enestrom–Kakeya stability conditions.

AMS Subject Classification: 39A11, 34K20.Keywords: Volterra equations, stability, convexity.This is joint work with Vitaliy Gilyazev.

100

Existence of unbounded solutions

in rational equations

YEVGENIY KOSTROV

University of Rhode Island



[email protected]

We exhibit a range of parameters and a set of initial conditions where the rational differenceequation

xn+1 =

α+2k∑i=0

βixn−i

A+k∑

j=0

B2jxn−2j

has unbounded solutions.

AMS Subject Classification: 39A10, 39A11.Keywords: Existence of unbounded solutions, rational difference equation.This is joint work with E. Camouzis, E. A. Grove, and G. Ladas.

101

Solution to integral equations on time scales:

Existence, uniqueness and successive approximations

TOMASIA KULIK

University of New South Wales

School of Mathematics and Statistics

Sydney, Australia

[email protected]

http://web.maths.unsw.edu.au/˜tomasia

I will present my research on applying Banach’s and Granas’s fixed point theory to establishtheorems with sufficient conditions for existence, uniqueness of solutions to integral equations ontime scales, as well as methods of successive approximation to find the solution to any desiredaccuracy.

In particular, I will discuss integral equations on time scales over unbounded intervals andapplications of the results to examining and finding solutions of dynamic or integro-differentialequations on time scales and the additional conditions requited for existence and uniqueness inthese problems.

I will discuss applications of dynamic equations on time scales, to modeling various dynam-ical systems with complex dynamics, which varies continuously part of the time and discretelypart of the time.

This is joint work with Christopher C Tisdell.

102

Linear kth order functional and difference equations

in the space of strictly monotonic functions

JITKA LAITOCHOVA

Palacky University

Department of Mathematics, Faculty of Education

Olomouc, Czech Republic

[email protected]

Abel functional equations are associated to a linear homogeneous functional equation withconstant coefficients. The work uses the space S of continuous strictly monotonic functions Φ :(−∞,∞) → (a, b) equipped with a multiplication f g = fX−1g, the symbol X being a pre-selected canonical function in S. Because of the space S, classical terms like composite function,iterates of a function, Abel functional equation and linear homogeneous functional equation, mustbe re-defined.

We consider the functional equation

akf Φk(x) + · · ·+ a0f Φ0(x) = 0,

which is solved using roots of the characteristic equation and a continuous solution of the Abelfunctional equation

α Φ(x) = X(x+ 1) α(x).

The classical theory of linear homogeneous functional and difference equations is obtained as aspecialization of the theory in space S. All functional equation results apply to difference equa-tions.

AMS Subject Classification: 39B05, 39B12.Keywords: Difference equation, functional equation.

103

The Marshall differential analyzer:

Dynamic equations in motion!

BONITA LAWRENCE

Marshall University


Huntington, West Virginia, USA

[email protected]

http://www.science.marshall.edu/lawrence

The Marshall University differential analyzer team has completed the construction of a fourintegrator, primarily mechanical differential analyzer. Machines of this type, first built in the late1920s and the early 1930s, were designed to solve differential equations and plot the solutions.Our machine, known to the team as “Art”, is modeled after the first differential analyzer built inEngland and named for its builder, Dr. Arthur Porter. It is built almost exclusively from Meccanoor (Meccano type) components and was constructed by a team of undergraduate and graduatestudents from Marshall University. This talk will begin with a discussion of the constructionof the machine and its fundamental components. The machine offers a fantastic physical andvisual interpretation of a differential equation. How this visualization is achieved through thefundamental mechanics and the programming of the machine will then be addressed. Examplesof machine setups will be presented.

AMS Subject Classification: 34.Keywords: Dynamic equations, differential analyzer.

104

Nonautonomous periodic systems with Allee effect

RAFAEL LUIS

Center for Mathematical Analysis and Dynamical Systems


Lisbon, Portugal

[email protected]

http://members.netmadeira.com/rafaelluis

We introduce a new class of maps, called unimodal Allee maps (UAM). These maps arise inthe study of population dynamics in which the system has three fixed points, a stable fixed pointzero, an unstable positive fixed point (Allee point) and a stable positive fixed point (carryingcapacity). We analyse the properties of the Allee points and the carrying capacity and establishtheir stability, for nonautonomous periodic systems formed by unimodal Allee maps.

Keywords: Allee effect, Allee point, carrying capacity, UAM.This is joint work with Saber Elaydi and Henrique Oliveira.

105

Ostrowski inequalities on time scales

THOMAS MATTHEWS




[email protected]

The presentation contains proofs of Ostrowski inequalities (regular and weighted cases) ontime scales and thus unifies and extends corresponding continuous and discrete versions fromthe literature. An application to the quantum calculus case will also be provided.

This is joint work with Martin Bohner.

106

Numerical detection of explosions and asymptotic

behaviour of delay-differential equations

MICHAEL MCCARTHY

Dublin City University


Dublin, Ireland

[email protected]

http://student.dcu.ie/˜mccarm29/index.html

In this talk we study scalar delay-differential equations whose solutions explode in finitetime. Our goal is to devise a discretisation of the equation such that: (i) the discrete equation “ex-plodes”; (ii) the rate at which the explosion occurs is preserved by discretising; (iii) the explosiontime can be approximated arbitrarily well by making a sufficiently large computational effort.

We show that these goals are all achieved by making an adaptive time-discretisation wherethe length of the step size tends to zero as the explosion time is approached. The same adap-tive method also reproduces the asymptotic behaviour of rapidly growing solutions of a similarclass of nonexploding equations: Therefore, the method does not induce spurious explosions notpresent in continuous time.

The work is joint with John Appleby and is supported by the IRCSET Embark Initiativeunder the project “Explosions in stochastic dynamical systems applied to finance”.

Keywords: Delay differential equation, explosions.This is joint work with John Appleby.

107

Learning to play Nash in

deterministic uncoupled dynamics

VIVALDO MENDES

ISCTE

Department of Economics

Lisbon, Portugal

[email protected]

In a boundedly rational game, where players cannot be as super-rational as in Kalai andLeher (1993), are there simple adaptive heuristics or rules that can be used in order to secure con-vergence to Nash equilibria? Young (2008) argues that if an adaptive learning rule obeys threeconditions – (i) it is uncoupled, (ii) each player’s choice of action depends solely on the frequencydistribution of past play, and (iii) each player’s choice of action, conditional on the state, is deter-ministic – no such rule leads the players’ behavior to converge to Nash equilibra. In this paperwe present a counterexample, showing that there are in fact simple adaptive rules that secureconvergence in a fully deterministic and uncoupled game. We used the Cournot model with non-linear costs and incomplete information for this purpose and also illustrate that the convergenceto Nash equilibria can be achieved with or without any coordination of the players actions.

AMS Subject Classification: 91A25, 91A26, 91A50.Keywords: Uncoupled dynamics, Nash equilibrium, convergence.This is joint work with Orlando Gomes and Diana Mendes.

108

Time scale extensions of a theorem of Wintner

on systems with asymptotic equilibrium

RAZIYE MERT



Ankara, Turkey

[email protected]

http://www.metu.edu.tr/˜raziye

We consider quasilinear dynamic systems of the form

x∆ = A(t)x+ f(t, x), t ∈ [a,∞)T,

where T is a time scale, and extend theorems obtained for differential equations by Trench [SIAMJ. Math. Anal.] to dynamic equations on time scales; thus provide extensions of a theorem ofWintner on systems with asymptotic equilibrium to time scales. In particular, we give sufficientconditions for the asymptotic equilibrium of the above system in the sense that there is a solutionsatisfying

limt→∞

x(t) = c

for any given constant vector c. Our results are new for difference and q-difference equations eventhough their analogues for differential equations have been known for some time.

Keywords: Asymptotic equilibrium, dynamic system, time scales.This is joint work with Agacık Zafer.

109

A new approach for solving Fredholm

integro-difference equations

HAMID MESGARANI

Shahid Rajaee University


Tehran, Iran

[email protected]

The Taylor expansion approach to solve higher-order linear difference equations has beengiven by Sezer. In this paper, we modify and develop for solving the Fredholm integro-differenceequation. Also, examples that illustrate the pertinent features of the method are presented andthe results are discussed.

Keywords: Integro-difference, Fredholm, Taylor expansion.This is joint work with M. Shahrezaee.

110

Algebro-geometric solutions of the

Ablowitz–Ladik hierarchy

JOHANNA MICHOR

New York University

Courant Insitute of Mathematical Sciences

New York, New York, USA

[email protected]

http://www.mat.univie.ac.at/˜jmichor

Algebro-geometric solutions of soliton equations are a class of solutions which can be con-structed explicitly using tools from algebraic geometry. We present a derivation of all algebro-geometric finite-band solutions of the Ablowitz–Ladik equation, which is a complexified versionof the discrete nonlinear Schrodinger equation.

In addition, we survey a recursive construction of the associated Ablowitz–Ladik hierarchy,a completely integrable sequence of systems of nonlinear evolution equations on the lattice Z.This is done by means of a zero-curvature and Lax approach.

AMS Subject Classification: 37K10, 37K15, 35Q55.Keywords: Discrete NLS, algebro-geometric solution, Lax pair.This is joint work with Fritz Gesztesy, Helge Holden, and Gerald Teschl.

111

Oscillatory and asymptotic properties of solutions

of nonlinear neutral-type difference equations

MAŁGORZATA MIGDA

Poznan University of Technology

Institute of Mathematics

Poznan, Poland

[email protected]

http://www.math.put.poznan.pl/˜mmigda

We consider higher-order neutral difference equations of the form

∆m(xn + pnxn−τ ) = f(n, xn, xσ(n)) + hn,

where m ≥ 2, (pn), (hn) are sequences of real numbers, τ is a nonnegative integer, (σ(n)) is aninteger sequence with σ(n) ≤ n and lim

n→∞σ(n) = ∞, f : N× R× R → R.

The study of asymptotic behavior of solutions of nonlinear equations of this type often re-quires that the sequence (pn) satisfies pn > 0 or pn < 0. We examine the case when (pn) is anoscillatory sequence.

AMS Subject Classification: 39A10, 39A11.This is joint work with Janusz Migda.

112

An example of a strongly invariant, pinched core strip

LEOPOLDO MORALES



Barcelona, Spain

[email protected]

In [Roberta Fabbri, Tobias Jager, Russel Johnson, Gerhard Keller, A Sharkovskii-type the-orem for minimally forced interval maps, Topological Methods in Nonlinear Analysis, volume26, number 1, pages 163–188, 2005], the authors define the concept of Pinched core strip. So far ithas not been given an example of such an object that is strongly invariant under a quasi-periodictriangular function and it is not a curve. In this talk we will describe how to construct such anexample.

This is joint work with Lluıs Alseda and Francesc Manosas.

113

Numerical solutions of nonlinear

differential-difference equations by the

variational iteration method

VOLKAN OBAN

Ege University


Izmir, Turkey

[email protected]

We extend He’s variational iteration method to find approximate solutions for nonlineardifferential-difference equations such as Volterra’s equation. A simple but typical example is ap-plied to illustrate the validity and great potential of the generalized variational iteration methodin solving nonlinear differential-difference equations. The results reveal that the method is veryeffective and simple. We find the extended method for nonlinear differential-difference equationsis of good accuracy.

Keywords: He’s variational iteration method, differential-difference, Volterra equation.This is joint work with Ahmet Yıldırım.

114

Solution spaces of dynamic equations

over time scales space

RALPH OBERSTE-VORTH

Marshall University


Huntington, West Virginia, USA

[email protected]

http://www.marshall.edu/math/contact.asp

We prove a recent conjecture characterizing the Fell topology on the space of time scales. Wepursue basic questions of how a changes in time scale may affect the solutions of a given dynamicequation. Insight into these questions are of interest both for applications as well as in theory.

AMS Subject Classification: 37.Keywords: Time scales, dynamic equation, Fell topology.

115

Bifurcations for nonautonomous interval maps

HENRIQUE OLIVEIRA

Instituto Superior Tecnico Lisbon


Lisbon, Portugal

[email protected]

http://www.math.ist.utl.pt/˜holiv

In this work we investigate attracting periodic orbits for nonautonomous discrete dynamicalsystems with two maps using a new approach. We study some types of bifurcation in these sys-tems. We show that the pitchfork bifurcation plays an important role in the creation of attractingorbits in families of alternating systems with negative Schwarzian derivative and it is central inthe geometry of the bifurcation diagrams.

AMS Subject Classification: Primary: 37E05; Secondary: 37E99.Keywords: Nonautonomous system, bifurcation.This is joint work with Emma D’Aniello.

116

On the spectrum of normal

difference operators of first order

RUKIYE OZTURK

Karadeniz Technical University


Trabzon, Turkey

[email protected]

In this talk the normality and spectrum of some first order difference operators in the Hilbertspace of sequences l2(N) are investigated. For example, a result has been established in the fol-lowing form.

Let S and A be respectively a right shift and a linear self-adjoint operator in the space l2(N)and (ImS)l2(N) ⊂ D(A). Then

1. The operator L = 1 − S + A, L : D(A) ⊂ l2(N) → l2(N) is normal in l2(N) if and only ifA = f(ImS) (here f is a function from σ(ImS) to R).

2. If L = 1 − S + A, L : D(A) ⊂ l2(N) → l2(N) is a normal operator and A − S = h(ImS),h : σ(ImS) → C, h ∈ C(σ(ImS)), then the spectrum of the operator L is the form σ(L) =(1 + h)([−1, 1]).

AMS Subject Classification: 47A10.Keywords: Space of sequences, difference operators.This is joint work with Zameddin Ismailov.

117

Boundedness, attractivity, stability of a rational

difference equation with two periodic coefficients

GARYFALOS PAPASCHINOPOULOS

Democritus University of Thrace

Department of Environmental Engineering

Xanthi, Greece

[email protected]

We study the boundedness, the attractivity and the stability of the positive solutions of therational difference equation

xn+1 =pnxn−2 + xn−3

qn + xn−3, n = 0, 1, . . . ,

where pn, qn, n = 0, 1, . . . are positive sequences of period 2.

AMS Subject Classification: 39A10.Keywords: Difference equation, boundedness, stability.This is joint work with G. Stefanidou and C. J. Schinas.

118

Classification and stability of functional equations

CHOONKIL PARK

Hanyang University


Seoul, South Korea

[email protected]

In this talk, we classify and prove the generalized Hyers–Ulam stability of linear, quadratic,cubic, quartic and quintic functional equations in complex Banach spaces.

AMS Subject Classification: 39B72.Keywords: Fixed point, functional equations, stability.This is joint work with Young Hak Kwon.

119

Bounded solutions of a rational difference equation

SANDRA PINELAS

Azores University

Mathematical Department

Ponta Delgada, Portugal

[email protected]

http://www.uac.pt/˜spinelas

This talk studies the existence of bounded solutions of the rational difference equation

xn+1 =βnxn + xn−1

xn−2, n = 1, 2, . . .

with initial conditions x−2, x−1, x0 ∈ R+ and 0 < βn < 1.

120

Nonoscillatory solutions of a second-order

difference equation of Poincare type

MIHALY PITUK

University of Pannonia

Department of Mathematics and Computing

Veszprem, Hungary

[email protected]

http://www.szt.vein.hu/˜pitukm

Poincare’s classical theorem about the convergence of the ratios of successive values of thesolutions of linear homogeneous difference equations applies if the characteristic values of thelimiting equation are simple and have different moduli. In this talk we show that for the nonoscil-latory solutions the conclusion of Poincare’s theorem is also true in the case when the limitingequation has a double positive characteristic value.

This is joint work with Rigoberto Medina.

121

Generalized Jacobians for solving nondifferentiable

equations arising from contact problems

NICOLAE POP

North University of Baia Mare


Baia Mare, Romania

[email protected]

http://www.ubm.ro

The aim of this talk is to give an algorithm for solving nondifferentiable equations usinggeneralized Jacobians with applications in contact problems. In contact problems, the functionalwhich describes the influence of the friction is nondifferentiable. For solving the discretized con-tact problem, the Newton method for linearization is employed, where generalized Jacobiansmust be used. The generalized Jacobians and the generalized gradient coincide. This method canbe used to apply the conjugate gradient method for solving of the equation that contains a non-differentiable nonlinear operator which is reduced to the successive solution of auxiliary linearequations. This linear operator (equations) can be regarded as a special kind of preconditioner.See also Axelson, O., Chronopoulos, A. T., On nonlinear generalized conjugate gradient methods,Numer. Math., 69 (1994), No. 1, pp. 1–15 and Clarke, F. H., Optimization and nonsmooth analysis,Wiley and Sons, 1983.

AMS Subject Classification: 35J85, 74G15.Keywords: Generalized Jacobian, contact problems.

122

Integro-difference equation associated

to a reaction-diffusion equation

EMIL POPESCU

Technical University of Bucharest

Civil Engineering

Bucharest, Romania

[email protected]

Using a product formula and the discretization of the time for a reaction-diffusion equa-tion, we present a sequential splitting schema which gives corresponding discrete time integro-difference equation.

This is joint work with Nedelia Antonia Popescu.

123

Finite size scaling technique and applications

NEDELIA ANTONIA POPESCU

Romanian Academy of Sciences

Astronomical Institute

Bucharest, Romania

[email protected]

The finite size scaling technique is applied on the Ulysses/VHM data in order to study thescaling of the magnetic field magnitude (B) and energy density (B2) fluctuations of the interplan-etary magnetic field.

The basic considered quantity is the change in the normalizedB,B(t)/〈B〉, at different scales(time lags) τn = 2n (days), n = 0, 1, 2, . . . as follows:

dBn = dBn(ti, τn) = [B(ti + τn)−B(ti)] /〈B〉,

where ti is the time (day); < B > is the average of B over 1 year at a specific distance; B(ti) is thedaily average of B.

This is joint work with Emil Popescu.

124

Dynamic replicator equation and its transformation

ZDENEK POSPISIL

Masaryk University



[email protected]

http://www.math.muni.cz/˜pospisil

The replicator equation is a vector ordinary differential equation with a cubic nonlinearity. Itprovides a description of game dynamics as well as evolutionary models for population genetics.The contribution introduces a dynamic replicator equation for Sn valued function x(t) =

(xi(t)

):

x∆i (t) = xi(t)

(n∑

k=1

aikxσi (t)− x(t)TAxσ(t)

), i = 1, 2, . . . , n;

here A = (aij) is an n × n real matrix and Sn is the n-dimensional probability simplex. Basicqualitative properties of the solution will be shown. The main result is that under some assump-tions, there exists a time scale such that the replicator equation is equivalent to the Lotka–Volterradynamic equation

y∆j (τ) = yj(τ)

(rj +

n−1∑k=1

bjkyσk (τ)

), j = 1, 2, . . . , n− 1

for y(τ) =(yj(τ)

)from positive (n− 1)-dimensional orthant.

AMS Subject Classification: 34A34, 39A12, 92B05.Keywords: Dynamic nonlinear equation, transformation.

125

Nonautonomous continuation

and bifurcation, revisited!

CHRISTIAN POTZSCHE

Munich University of Technology

Center for Mathematical Sciences

Munich, Germany

[email protected]

http://www-m12.ma.tum.de/poetzsche

We investigate local continuation and bifurcation properties for nonautonomous differenceequations. Due to their arbitrary time dependence, equilibria or periodic solutions typically donot exist and are replaced by bounded globally defined solutions.

Following this leitmotiv, hyperbolicity properties are formulated via the Sacker–Sell spec-trum and exponential dichotomies yield a robust framework for local continuation arguments us-ing the (surjective) implicit function theorem. Dichotomies in variation also provide a Fredholmtheory. Thus, we employ a Lyapunov–Schmidt-reduction to deduce nonautonomous versions ofthe classical fold, transcritical and pitchfork bifurcation patterns.

Finally, Sacker–Sell spectral intervals crossing the stability boundary give rise to a new 2-stepbifurcation pattern not present in the autonomous situation.

Keywords: Nonautonomous bifurcation, Sacker–Sell spectrum.

126

A nonlinear system of difference equations

MIHAELA PREDESCU

Bentley College

Department of Mathematical Sciences

Waltham, Massachusetts, USA

[email protected]

http://web.bentley.edu/empl/p/mpredescu

We investigate the global stability character and the behavior of solutions of the nonlinearsystem of difference equations

Mn+1 = aMn + bHn(1− e−Mn)

Hn+1 = cHn

1+pAn+ 1

1+qAn

An+1 = rAn +Mn,

n = 0, 1, . . . .

The initial conditions are nonnegative, the parameters are positive and a, c, r ∈ (0, 1).

AMS Subject Classification: 39A11.This is joint work with T. Awerbuch, E. Camouzis, E. A. Grove, G. Ladas, and R. Levins.

127

Galerkin method for solving nonlinear

Fredholm–Hammerstein integral equations

with multiwavelet basis

MOHSEN RABBANI

Islamic Azad University, Sari Branch


Sari, Iran

[email protected]

In this talk, we solve nonlinear Fredholm–Hammerstein integral equations by using multi-wavelets constructed from Legendre polynomials. For reducing the operations in comparing withsimilar works, we used some modifications in approximation coefficients calculating scheme. Thenumerical examples for the method are of good accuracy.

Keywords: Multiwavelet, Fredholm–Hammerstein, nonlinear.

128

On some rational difference equations via

linear recurrence equations properties

MUSTAPHA RACHIDI

LEGT - F. Arago. Academie de Reims

Mathematics Section

Reims, France

[email protected]

The purpose of this talk is to examine the local stability of the following class of rationaldifference equations

xn+1 =∑k−1

i=0 aixn−i−1∑k−1i=0 bixn−i−1

, (1)

where ai ≥ 0, bi ≥ 0 (i = 0, 1, . . . , k) and the initial conditions x−k, x−k+1, . . . , x0 are arbitraryreal numbers. The approach used here is based on the properties of the linear recurrence partassociated to equation (1). More precisely, we consider some properties on the convergence oflinear recursive sequences, which permits us to obtain some new results on the local stability ofequation (1). In addition, for a particular case of equation (1), a straightforward computationleads to the extension of some recent results concerning the global attractivity and boundednessof this equation.

Keywords: Difference equations, stability, recursiveness.This is joint work with Rajae Ben Taher and Mohamed El Fetnassi.

129

Multiple periodic solutions of a second-order

nonautonomous rational difference equation

MICHAEL RADIN

Rochester Institute of Technology


Rochester, New York, USA

[email protected]

http://www.rit.edu/cos/math/Directory/

→Standard/marsma.html

We will investigate the existence of multiple periodic solutions of a second order nonau-tonomous rational difference equation. We will discover the necessary and sufficient conditionsfor existence of multiple periodic solutions, the pattern of the periodic solutions and convergenceto zero and to multiple periodic solutions.

AMS Subject Classification: 39A.Keywords: Convergence, periodic solutions, boundedness.This is joint work with Nicholas Batista.

130

Morse spectrum for linear

nonautonomous difference equations

MARTIN RASMUSSEN

University of Augsburg


Augsburg, Germany

[email protected]

http://www.math.uni-augsburg.de/˜rasmusse

In this talk, the concept of a Morse spectrum is introduced for nonautonomous linear dif-ference equations. In contrast to other spectral notions such as the Sacker-Sell spectrum (whichyields a linear decomposition), the Morse spectrum is based on a linear decomposition, the finestMorse decomposition. The existence of such a Morse decomposition is reviewed, and basic prop-erties of the Morse spectrum are discussed. The content of this talk is based on joint work withFritz Colonius (University of Augsburg) and Peter Kloeden (University of Frankfurt).

This is joint work with Fritz Colonius and Peter Kloeden.

131

Power type comparison theorems for

half-linear dynamic equations

PAVEL REHAK

Academy of Sciences of the Czech Republic



[email protected]

http://www.math.muni.cz/˜rehak

We establish conditions which guarantee that oscillatory properties of a half-linear dynamicequation are preserved when the power in the nonlinearities is changed. We discuss the discrep-ancies between the results on different time scales. The results are original also in the differentialand difference equations cases.

132

Decoupling and simplifying of discrete dynamical

systems in the neighbourhood of invariant manifold

ANDREJS REINFELDS

University of Latvia

Institute of Mathematics and Computer Science

Riga, Latvia

[email protected]

http://home.lanet.lv/˜reinf

In a Banach space X×E, the discrete dynamical systemx(t+ 1) = g(x(t)) +G(x(t), p(t)),

p(t+ 1) = A(x(t))p(t) + Φ(x(t), p(t))(1)

is considered. Sufficient conditions under which there is an Lipschitzian invariant manifoldu : X → E are obtained. Using this result we find sufficient conditions of conjugacy of (1) andx(t+ 1) = g(x(t)) +G(x(t), u(x(t)),

p(t+ 1) = A(x(t))p(t).

Relevant results concerning partial decoupling and simplifying of the semidynamical systems aregiven also.

AMS Subject Classification: 39A, 37D30, 34C31.Keywords: Conjugacy, dynamical systems, invariant manifold.

133

On oscillation of solutions of stochastically

perturbed difference equations

ALEXANDRA RODKINA

University of the West Indies


Kingston, Jamaica

[email protected]

http://www.mona.uwi.edu/dmcs/staff/

→arodkina/alya.htm

We discuss the path-wise oscillatory behavior of the scalar nonlinear stochastic differenceequation

X(n+ 1) = X(n)− f(X(n)) + g(n,X(n))ξ(n+ 1), n = 0, 1, . . . ,

with nonrandom initial value X0 ∈ R. Here (ξ(n))n≥0 is a sequence of independent randomvariables with zero mean and unit variance. The functions f : R → R and g : N × R → Rare presumed to be continuous. We consider state-independent perturbation, when g does notdepend on the second variable, as well as the state-dependent perturbation.

AMS Subject Classification: 37H10, 39A11, 60H10, 34F05, 65C20.Keywords: Stochastic difference equations, oscillation.

134

Invariant objects through wavelets

DAVID ROMERO I SANCHEZ



Bellaterra (Cerdanyola del Valles), Spain

[email protected]

http://www.gsd.uab.cat/personal/dromero

A standard approach used in the literature to compute and work with invariant objects ofsystems exhibiting periodic or quasi-periodic behaviour is to use finite Fourier approximations,namely

F(ξ) = a0 +N∑

n=1

(an cos(nξ) + bn sin(nξ)) .

Finite wavelet expansions could be used instead,

F(ξ) =N∑

j=0

Nj∑n=0

cj,nψj,n(ξ),

where ψj,n(ξ) is obtained by translation and dilation of a mother wavelet ψ(x).

Since wavelets can capture different frequencies at different regions of the space, this ap-proach is expected to be more efficient than the Fourier one. The aim of this talk is to comparethe (computional) efficiency of both approaches. For that, we will briefly introduce the necessarytools for wavelet basis and multiresolution analysis.

This is joint work with Lluıs Alseda and Josep M. Mondelo.

135

Compatibility of local and global stability conditions

for some discrete population models

SAMIR SAKER

King Saud University


Riyadh, Saudi Arabia

[email protected]

In this talk, we consider a model that has been proposed to study the growth of bobwhitequail populations of Northern Wisconsin and prove that the local stability implies the globalstability. We will prove the results by using a suitable Lyapunov function and for illustrationwe apply the results on the Hassell and Smith models. We will show that for different values ofthe parameters, the population will exhibit some time varying dynamics. For parameters closeto stable region, this will be a simple two-cycle and if the system is moved in a direction awayfrom stability, by increasing the parameters then the dynamics become more complex and thesystem undergoes a series of bifurcations which leading to increasingly longer periodic cycles andfinally deterministic chaos. Some illustrative examples and graphs are included to demonstratethe validity and applicability of the results.

AMS Subject Classification: 39A10, 92D25.Keywords: Local, global stability, population dynamics.

136

Discrete densities and Fisher information

PABLO SANCHEZ-MORENO

University of Granada

Institute Carlos I for Theor. and Comput. Physics

Granada, Spain

[email protected]

http://www.ugr.es/˜pablos

Analytic information theory of discrete distributions was initiated in 1998 by C. Knessel,P. Jacquet and S. Szpankowski who addressed the precise evaluation of the Renyi and Shannonentropies of the Poisson, Pascal (or negative binomial) and binomial distributions. They wereable to derive various asymptotic approximations and, at times, lower and upper bounds forthese quantities. Here we extend these investigations in a twofold way. First, we consider amuch larger class of distributions, involving discrete hypergeometric-type polynomials which areorthogonal with respect to the weight function of Poisson, Pascal, binomial and hypergeometrictypes; that is the polynomials of Charlier, Meixner, Kravchuck and Hahn. Second we compute, attimes explicitly, the Fisher informations of the four families of these Rakhmanov distributions.

AMS Subject Classification: 62B10, 30G25.Keywords: Fisher information, discrete densities.This is joint work with J. S. Dehesa, R. J. Yanez.

137

Boundedness, periodicity, attractivity of the

difference equation xn+1 = An +(

xn−1xn

)p

CHRISTOS SCHINAS


Department of Electrical and Computer Engineering

Xanthi, Greece

[email protected]

http://utopia.duth.gr/˜cschinas

This talk studies the boundedness, the persistence, the periodicity and the stability of thepositive solutions of the nonautonomous difference equation

xn+1 = An +(xn−1

xn

)p

, n = 0, 1, . . . ,

where An is a positive bounded sequence, p ∈ (0, 1) ∪ (1,∞) and x−1, x0 ∈ (0,∞).

AMS Subject Classification: 39A10.Keywords: Boundedness, persistence, periodicity, stability.This is joint work with G. Papaschinopoulos and G. Stefanidou.

138

Oscillation of nonlinear

three-dimensional difference systems

EWA SCHMEIDEL

Poznan University of Technology


Poznan, Poland

[email protected]

http://www.put.poznan.pl/˜schmeide

Oscillatory properties of solutions are investigated usually for two-dimensional differencesystems only, but we have not seen too many oscillatory results for three-dimensional systemsof the general form. This observation motivated us to consider nonlinear three-dimensional dif-ference systems and to investigate its oscillatory or almost oscillatory behavior. Moreover, it isan interesting problem to extend oscillation criteria for third-order nonlinear difference equationsto the case of nonlinear three-dimensional difference systems since such systems include, in par-ticular, third-order nonlinear difference equations as a special case. We shall provide sufficientconditions under which the considered system is oscillatory or almost oscillatory.

AMS Subject Classification: 39A10, 39A11.Keywords: Nonlinear difference system, oscillation.

139

On the behaviour of the difference equation

x(n + 1) = max1/x(n), min1, A/x(n)

NURCAN SEKERCI

Selcuk University


Konya, Turkey

[email protected]

We study the behavior of the solution of the difference equation

x(n+ 1) = max1/x(n),min1, A/x(n),

where A is a real number and the initial condition x(0) is a nonzero real number. In the cases ofA > 0 and A < 0 we determine the behaviour of the equation with A, x0.

AMS Subject Classification: 39A10, 39A11.Keywords: Difference equation, periodicity, behaviour.This is joint work with Necati Taskara and D. Turgut Tollu.

140

Heat solutions by using Fibonacci tane function

MOHSEN SHAHREZAEE

Imam Hossein University


Tehran, Iran

[email protected]

In this talk we introduce and use symmetrical Fibonacci tane for solving heat equation. Weknow the symmetrical Fibonacci tane is constructed according to the symmetrical Fibonacci sineand cosine in the model of

SFS(x) =αx − α−x

√5

CFS(x) =αx + α−x

√5

and tFS will be defined by

tFS(x) =αx − α−x

αx + α−x.

As one of its applications an algorithm is devised to obtain exact traveling heat solutions forthe differential-difference equations by means of the property of function tane. In fact, we havedevised a straightforward algorithm to compute traveling heat solutions without using explicitintegration.

141

Applications of finite difference methods

in the field of magnetic refrigeration

BAKHODIRZHON SIDDIKOV

Ferris State University


Big Rapids, Michigan, USA

[email protected]

http://www.ferris.edu/htmls/colleges/

→artsands/faculty desc.cfm?FSID=174

Magnetic refrigeration is rapidly developing and becoming competitive with conventionalgas compression technology, primarily because the most inefficient component of the refrigerator– the compressor – is eliminated. In this talk, we will discuss a time-dependent one-dimensionalmodel of the active magnetic regenerator which was developed as a highly nonlinear systemof partial differential equations. One of the difficulties in the numerical simulations of the activemagnetic regenerator is determination of the heat capacity of the magnetic material (gadolinium),C = C(T,H), which depends on the temperature of the material, T = T (x, t), as well as on themagnetic induction, H = H(t), where x is a spatial coordinate and t is a chronological coordi-nate. I will present an approximation surface for C = C(T,H), which was obtained by using theleast-squares surface fitting technique and experimental measurements at 460 data points. Wedeveloped the numerical scheme for the computer simulations of the active magnetic regeneratorby using a finite-difference method. We will analyze the performance of the numerical schemefor stability and convergence.

AMS Subject Classification: 47N.Keywords: Finite difference method, magnetic refrigeration.

142

Spectral theory of birth-and-death processes

MORITZ SIMON

Munich University of Technology


Munich, Germany

[email protected]

http://ibb.gsf.de/person.php?name=Moritz+Simon

This talk gives an outline of the author’s PhD thesis about birth–and–death processes withkilling [Moritz Simon, Spectral Theory of Birth-and-Death Processes, PhD thesis (TUM), Sierke Ver-lag, Gottingen, 2008]. Such stationary Markov processes admit a representation of their transitionprobabilities via orthogonal polynomials (OP) with respective spectral measure. The recursionof the OP depends purely on the birth, death and killing rates in the population process. Linearrates for instance admit an explicit computation of the OP and their spectral measure, which inturn allow to determine the stochastic dynamics of the process. Problems come in as soon as therates are sufficiently complicated: explicit methods are no more tractable then! Anyway, the useof regular perturbation theory for corresponding Jacobi operators enables one to determine thespectrum in qualitative and approximate respects, at least under a certain domination of killing.

143

Numerical solution of nonlocal boundary value

problems for the Schrodinger equation

ALI SIRMA

Bahcesehir University

Department of Mathematics and Computer Sciences

Istanbul, Turkey

[email protected]

In this talk the numerical solution of the multipoint nonlocal boundary value problemiut −

m∑r=1

(ar(x)uxr)xr

+ σuf(t, x), 0 < t < T, x ∈ Ω,

u(0, x) =p∑

j=1

αju(λj , x) + ϕ(x), x ∈ Ω,

u(t, x) = 0, ∂u(t,x)∂−→n = 0, x ∈ S, 0 ≤ t ≤ T,

for the Schrodinger equation is considered. Here, ar(x) (x ∈ Ω), ϕ(x) (x ∈ Ω), f(t, x) (t ∈ [0, T ],x ∈ Ω) are smooth functions and σ > 0 is a constant. Ω is the unit cube in the m-dimensionalEuclidean space Rm (0 < xk < 1, 1 ≤ k ≤ m) with boundary S and Ω = Ω ∪ S, −→n denotes thenormal vector to boundary S.

AMS Subject Classification: 65N14.Keywords: Schrodinger equation, stability.This is joint work with Allaberen Ashyralyev.

144

On a system of max-difference equations

GESTHIMANI STEFANIDOU


Department of Electrical and Computer Engineering

Xanthi, Greece

[email protected]

In this talk we study the periodic nature of the positive solutions of the system of differenceequations

yn = maxA1

zn−1,B1

zn−3,C1

zn−5

, zn = max

A2

yn−1,B2

yn−3,C2

yn−5

, n ≥ 0,

whereAi, Bi, Ci, i ∈ 1, 2, are positive real constants and the initial values yi, zi, i ∈ −5,−4, . . . ,−1are positive numbers. In addition, we give conditions so that the solutions of this system are un-bounded.

AMS Subject Classification: 39A10.Keywords: Difference equations, periodicity, unboundedness.This is joint work with G. Papaschinopoulos and C. J. Schinas.

145

Basic properties of partial dynamic operators

PETR STEHLIK

University of West Bohemia


Pilsen, Czech Republic

[email protected]

http://www.kma.zcu.cz/stehlik

Motivated by the importance of maximum principles in the theory of partial differentialequations and in numerical analysis, we establish simple maximum principles for basic partialdynamic operators on multidimensional time scales. As in the case of ordinary dynamic oper-ators we reveal a set of results and counterexamples which illustrate the distinct behaviour inthe continuous and discrete cases. Finally, we provide some immediate consequences and proveuniqueness results to problems involving partial dynamic operators.

This is joint work with Bevan Thompson.

146

Relative oscillation theory for Jacobi operators

GERALD TESCHL

University of Vienna

Faculty of Mathematics

Vienna, Austria

[email protected]

http://www.mat.univie.ac.at/˜gerald

Classical oscillation theory establishes the connection between the number of eigenvaluesand sign flips of certain solutions of a Jacobi operator respectively matrix. We add a new wrinkleto this theory by showing how the number of sign flips of Wronski (resp. Casorati) determinantsof solutions can be connected to differences of numbers of eigenvalues.

AMS Subject Classification: 39A10, 39A12.Keywords: Oscillation theory, Jacobi operators.

147

Reducibility and stability results for

linear systems of difference equations

AYDIN T IRYAKI

Gazi University


Ankara, Turkey

[email protected]

http://websitem.gazi.edu.tr/tiryaki

In this talk, we first give a theorem on the reducibility of a linear system of difference equa-tions of the form x(n+1) = A(n)x(n). Next, by means of Floquet theory, we obtain some stabilityresults. Moreover, some examples are given to illustrate the importance of the results.

AMS Subject Classification: 39A05, 39A11.Keywords: Reducibility, periodic matrix, Floquet exponents.This is joint work with Adil Mısır.

148

Analysis of a nonlinear discrete dynamical system,

signal coding and reconstruction

MOUHAYDINE TLEMCANI

Universidade de Evora

Centro de Geofısica de Evora (CGE)

Evora, Portugal

[email protected]

In this talk, we present a study of different iterated maps in which we are looking for in-variants that link their dynamics. Various approaches of conductivity of dynamical systems areanalyzed looking for real physical examples. The notion of conductance of a discrete nonlineardynamical system is linked to a physical time dependent example. The time series issued froma physical system behaviour are processed from a new point of view in order to extract hiddeninformation.

AMS Subject Classification: 37B10, 37A35.Keywords: Dynamical systems, conductance, time series.This is joint work with Sara Fernandes.

149

Multiple positive solutions for a system of

higher-order boundary value problems on time scales

FATMA SERAP TOPAL

Ege University


Izmir, Turkey

[email protected]



In this talk, by applying fixed point theorems in cones and under suitable conditions, wepresent the existence of single and multiple solutions for the following system of higher-orderboundary value problems:

(−1)ny42n

1 (t) = f1(t, yσ1 (t), yσ

2 (t)), t ∈ [0, 1],

(−1)my42m

2 (t) = f2(t, yσ1 (t), yσ

2 (t)), t ∈ [0, 1],

y42i

1 (0) = y42i

1 (σ(1)) = 0, 0 ≤ i ≤ n− 1,

y42j

2 (0) = y42j

2 (σ(1)) = 0, 0 ≤ j ≤ m− 1.

AMS Subject Classification: 39A10, 34B15, 34A40.Keywords: Positive solutions, cone, fixed point theorems.This is joint work with Erbil Cetin.

150

Positive solutions of a second-order

m-point BVP on time scales

AHMET YANTIR

Atılım University


Ankara, Turkey

[email protected]

http://www.atilim.edu.tr/˜ayantir

In this study, we are concerned with proving the existence of multiple positive solutions of ageneral second-order nonlinear m-point boundary value problem

u∆∇(t) + a(t)u∆(t) + b(t)u(t) + λh(t)f(t, u) = 0, t ∈ [0, 1],

u(ρ(0)) = 0, u(σ(1)) =m−2∑i=1

αiu(ηi)

on time scales. The proofs are based on fixed point theorems in a Banach space. We present anexample to illustrate how our results work.

AMS Subject Classification: 39A10, 34B18, 34B40, 45G10.Keywords: Multi-point BVPs, positive solutions, time scales.This is joint work with Fatma Serap Topal.

151

Numerical solutions of nonlinear

differential-difference equations

by the homotopy perturbation method

AHMET YILDIRIM

Ege University


Izmir, Turkey

[email protected]



A new scheme, deduced from He’s homotopy perturbation method, is presented for solvingdifferential-difference equations. A simple but typical example is applied to illustrate the valid-ity and great potential of the generalized homotopy perturbation method in solving differential-difference equations. The results reveal that the method is very effective and simple.

Keywords: He’s homotopy perturbation method, differential-difference, Volterra equation.This is joint work with Gulcin Yalazlar.

152

A result on successive approximation of solutions to

dynamic equations on time scales

ATIYA ZAIDI


School of Mathematics and Statistics

Sydney, Australia

[email protected]

http://www.maths.unsw.edu.au/˜atiya

We establish a Picard–Lindelof theorem for first order initial value problems on time scales,where a time scale is a nonempty closed subset of reals. The theorem involves sufficient condi-tions under which a problem will have a unique solution. At the heart of the approach is themethod of successive approximations. The investigation relies on ideas from classical analysisrather than functional analysis.

The results guarantee that the “error” estimate between the actual and the approximate so-lution goes to zero as the number of iterations are increased indefinitely.

An example regarding the application of the above method to a nonlinear dynamic equationon time scales is also presented. Several open questions will be posed that concern successive ap-proximations in the time scale setting. This talk will be suitable particularly for graduate students.

Keywords: Time scales, successive approximations, dynamic equation.This is joint work with Christopher Tisdell.

153

Application of the WKB estimation method for

determining heat flux on the boundary

ALI ZAKERI

K. N. Toosi University


Tehran, Iran

[email protected]

This talk considers a linear one-dimensional inverse heat conduction problem with noncon-stant thermal diffusivity. It has been associated with the estimation of an unknown boundaryheat flux. For this purpose, by using temperature measurements taken below the boundary sur-face and using a semi-implicit finite difference method, the problem will be converted to a systemof ordinary differential equations of second order depending on a small parameters with initialconditions. Then WKB estimation method gives asymptotic solutions for this system. The solu-tions that are produced in this algorithm make the process ill-posed. Then by choosing suitablevalues of small parameters, this algorithm is modified. Finally, a numerical experiment will bepresented.

AMS Subject Classification: 35R30.Keywords: Inverse problem, implicit finite difference method.

154

Trigonometric and hyperbolic systems on time scales

PETR ZEMANEK

Masaryk University



[email protected]

http://www.math.muni.cz/˜xzemane2

In this talk we discuss trigonometric and hyperbolic systems on time scales. These systemsgeneralize and unify their corresponding continuous-time and discrete-time analogues, namelythe systems known in the literature as trigonometric and hyperbolic linear Hamiltonian systemsand discrete symplectic systems. We provide time scale matrix definitions of the usual trigono-metric and hyperbolic functions and show that many identities known from the basic calculusextend to this general setting, including the time scale differentiation of these functions.

AMS Subject Classification: 39A12.Keywords: Time scale, Hamiltonian system, trigonometric system.This is joint work with Roman Hilscher.

155

Other Participants

157

THABET ABDELJAWAD

Cankaya University


Ankara, Turkey

[email protected]

http://math.cankaya.edu.tr/˜thabet

MELTEM ADIYAMAN

Dokuz Eylul University


Izmir, Turkey

[email protected]

MURAT AKMAN



Ankara, Turkey

[email protected]

158

MELTEM ALTUNKAYNAK



Ankara, Turkey

[email protected]

KEMAL AYDIN

Selcuk University


Konya, Turkey

[email protected]

MUJGAN BAS




[email protected]

159

MARTIN BOHNER




[email protected]

http://web.mst.edu/˜bohner

ILKNUR BOZOK

Atılım University


Ankara, Turkey

kuzu [email protected]

GULTER BUDAKCI



Izmir, Turkey

[email protected]

160

CANAN CAN

Atılım University


Ankara, Turkey

canan can [email protected]

DUYGU CAYLAK



Izmir, Turkey

duygu [email protected]

OKAY CELEBI

Yeditepe University


Istanbul, Turkey

[email protected]

http://www.math.metu.edu.tr/˜celebi

161

CEM CELIK



Izmir, Turkey

[email protected]

GULNUR CELIK KIZILKAN

Selcuk University


Konya, Turkey

[email protected]

http://asp.selcuk.edu.tr/asp/personel/


CENGIZ CINAR

Selcuk University


Konya, Turkey

[email protected]

162

SEBAHAT EBRU DAS

Yıldız Technical University


Istanbul, Turkey

[email protected]

ASLI DENIZ

Izmir Institute of Technology


Izmir, Turkey

[email protected]

ZHAOYANG DONG



Barcelona, Spain

[email protected]

163

MELDA DUMAN



Izmir, Turkey

[email protected]

SABER ELAYDI

Trinity University



[email protected]

http://www.trinity.edu/selaydi

MARIO GETIMANE

Instituto Superior de Transportes e Communicacoes


Maputo, Mozambique

[email protected]

164

IBRAHIM HALIL GUMUS

Selcuk University


Konya, Turkey

[email protected]

VEYSEL FUAT HATIPOGLU

Mugla University


Mugla, Turkey

[email protected]

GOKCE INTEPE



Izmir, Turkey

[email protected]

165

KHAJEE JANTARAKHAJORN

Thammasat University


Phatumthani, Thailand

[email protected]

http://math.sci.tu.ac.th/people 001.html

RUKIYE KARA

Mimar Sinan University


Istanbul, Turkey

[email protected]

ZEYNEP KAYAR



Ankara, Turkey

[email protected]

166

B ILLUR KAYMAKCALAN

Georgia Southern University



[email protected]

http://math.georgiasouthern.edu/˜billur

YELIZ KIYAK UCAR




[email protected]

SUPACHARA KONGNUAN




[email protected]


167

NATALIA KOSAREVA

Moscow Institute of Electronics and Mathematics

Cybernetics Department

Moscow, Russia

[email protected]

YAKOV KULIK


School of Physics

Sydney, Australia

[email protected]

V ILDAN KUTAY

Ankara University


Ankara, Turkey

vildan [email protected]

168

ANDREAS LEONHARDT

Technical University Munich


Munich, Germany

[email protected]

GORAN LESAJA

Georgia Southern University



[email protected]

ROBERT L. MARSH

East Georgia College

Mathematics / Science Division


[email protected]

http://personal.georgiasouthern.edu/˜rmarsh

169

ADIL MISIR

Gazi University


Ankara, Turkey

[email protected]

MEHMED NURKANOVIC

University of Tuzla


Tuzla, Bosnia and Herzegovina

[email protected]

http://www.pmf.untz.ba

ZEHRA NURKANOVIC

University of Tuzla


Tuzla, Bosnia and Herzegovina

[email protected]

http://www.pmf.untz.ba

170

OZKAN OCALAN




[email protected]

http://www2.aku.edu.tr/˜ozkan

ISRAFIL OKUMUS

Erzincan University


Erzincan, Turkey

[email protected]

UMUT MUTLU OZKAN




umut [email protected]

171

F IGEN OZPINAR




[email protected]

SERMIN OZTURK




[email protected]

ERSIN OZUGURLU



Istanbul, Turkey

[email protected]

172

PARAMEE REANKITTIWAT




[email protected]


ANDREAS RUFFING



Munich, Germany

[email protected]

http://www-m6.ma.tum.de/˜ruffing

IPEK SAVUN



Izmir, Turkey

ipek [email protected]

173

TUGCEN SELMANOGULLARI

Mimar Sinan University


Istanbul, Turkey

[email protected]

SOPORN SENEETANTIKUL




[email protected]


G IZEM SEYHAN

Ankara University


Ankara, Turkey

[email protected]

174

DAGISTAN S IMSEK

Selcuk University


Konya, Turkey

[email protected]



WALTER SIZER

Minnesota State University


Moorhead, Minnesota, USA

[email protected]

http://www.mnstate.edu/sizer

ANDREAS SUHRER



Munich, Germany

[email protected]

175

NECATI TASKARA

Selcuk University


Konya, Turkey

[email protected]

NAWALAX THONGJUB




[email protected]


D. TURGUT TOLLU

Selcuk University


Konya, Turkey

hasan [email protected]

176

DENIZ UCAR

Usak University


Usak, Turkey

[email protected]

MEHMET UNAL


Department of Software Engineering

Istanbul, Turkey

[email protected]

http://web.bahcesehir.edu.tr/munal

SIRICHAN VESARACHASART




[email protected]


177

DOMINIK VU

Vienna University of Technology

Institute of Analysis and Scientific Computing

Vienna, Austria

[email protected]

GULCIN YALAZLAR

Ege University


Izmir, Turkey

sugulu [email protected]

IBRAHIM YALCINKAYA

Selcuk University


Konya, Turkey

[email protected]



178

MUHAMMED Y IGIDER

Erzincan University


Erzincan, Turkey

m.yigider [email protected]

MUSTAFA KEMAL YILDIZ




[email protected]

OZLEM YILMAZ

Ege University


Izmir, Turkey

[email protected]

179

FULYA YORUK

Ege University


Izmir, Turkey

fulya [email protected]

180

Local Organization Assistants

181

M. ASLI AYDIN


Faculty of Arts and Sciences

Istanbul, Turkey

[email protected]

KEMAL BAYAT


Faculty of Engineering

Istanbul, Turkey

[email protected]

NAZLI CEREN DAGYAR



Istanbul, Turkey

[email protected]

182

YAKUP EMUL



Istanbul, Turkey

[email protected]

DURDANE ERKAL



Istanbul, Turkey

[email protected]

GOKCE KARAHAN



Istanbul, Turkey

[email protected]

183

MUSA KARAKELLE



Istanbul, Turkey

[email protected]

HUSEYIN OZDEMIR



Istanbul, Turkey

[email protected]

BAHADIR OZEN



Istanbul, Turkey

[email protected]

184

Conference Proceedings

The conference publishes refereed proceedings of accepted papers. The Proceedings are pub-lished by Ugur – Bahcesehir University Publishing Company (ISBN 978-975-6437-80-3). Contrib-utors receive the proceedings free of charge. The deadline to receive submissions prepared usingthe style file available from the conference website is October 31, 2008. The maximum page limitfor contributed talk papers is 8 printed pages. Please send the manuscript to the e-mail of theconference [email protected] or directly to any of the following editors.

Martin BohnerMissouri S&T


Zuzana DoslaMasaryk University




Mehmet UnalBahcesehir University

Istanbul, Turkey


Ankara, Turkey

185

Social Program

Sunday, July 20, 2008, 6 pm:

Bahcesehir University invites you to join the Welcome Party at the roof of the Besiktas buildingoverlooking the Bosporus. This event is included in the registration fee.

Monday, July 21, 2008, 6:15 pm:

Sightseeing, free time. Suggestions (on participants’ expenses): Visit to Dolmabahce Palace, Or-takoy, Taksim, Cicek Pasajı, and dinner in the Galata Tower.

Tuesday, July 22, 2008, 6:15 pm:

Sightseeing, free time (on participants’ expenses).

Wednesday, July 23, 2008, 9 am:

Istanbul tour (Topkapı Palace – Ayasofya Mosque – Archeology Museum). The Bosporus yachttour (on private yacht) including dinner starts at 7 pm and will take about 5 hours. The entire daytrip including all admission tickets and including the yacht tour is covered by the registration fee.

Thursday, July 24, 2008, 8 pm:

Bahcesehir University invites you to join the Farewell Dinner at the roof of the Besiktas buildingoverlooking the Bosporus. This event is included in the registration fee.

Friday, July 25, 2008, 6:15 pm:

More sightseeing, free time (on participants’ expenses).

187

Maps

ICDEA08 Staff meets you at the exit gate of Ataturk International Airport Terminal from 7:00 to23:30 on July 18–20, 2008 to help your transfer.

189

The conference site is on the Besiktas Campus of Bahcesehir University, on the European shoresof the Bosporus, a short walk from the ferry landing of the Besiktas (Europe) – Uskudar (Asia)connection (Besiktas Vapur Iskelesi).

190

The address of the Taslık Hotel is Suleyman Seba Caddesi No:75.

191

The address of the Yurdum Guest House (female) is Tavukcu Fethi Sokak No:29.

192

The address of the Yurdum Guest House (male) is Tas Basamak Sokak No:20.

193

About Istanbul

“There, God and human, nature and art are together, they have created such aperfect place that it is valuable to see.” Lamartine’s famous poetic line revealshis love for Istanbul, describing the embracing of two continents, with one armreaching out to Asia and the other to Europe.

Istanbul, once known as the capital of capital cities, has many unique fea-tures. It is the only city in the world to straddle two continents, and the only oneto have been a capital during two consecutive empires – Christian and Islamic.Once capital of the Ottoman Empire, Istanbul still remains the commercial, his-torical and cultural pulse of Turkey, and its beauty lies in its ability to embraceits contradictions. Ancient and modern, religious and secular, Asia and Europe,mystical and earthly all co-exist here.

Its variety is one of Istanbul’s greatest at-tractions: The ancient mosques, palaces, mu-seums and bazaars reflect its diverse history.The thriving shopping area of Taksim buzzeswith life and entertainment. And the serenebeauty of the Bosporus, Princes Islands andparks bring a touch of peace to the otherwisechaotic metropolis.Districts: Adalar, Avcilar, Bagcilar, Bahcelievler,Bakirkoy, Besiktas, Bayrampasa, Beykoz, Beyoglu, Eminonu, Eyup, Fatih, Gazi-osmanpasa, Kadıkoy, Kagithane, Kartal, Kucukcekmece, Pendik, Sarıyer, Sisli,Umraniye, Uskudar, Zeytinburnu, Buyukcekmece, Catalca, Silivri, Sile, Esenler,Gungoren, Maltepe, Sultanbeyli, Tuzla.

Golden Horn: This horn-shaped estuary di-vides European Istanbul. One of the best natu-ral harbours in the world, it was once the cen-tre for the Byzantine and Ottoman navies andcommercial shipping interests. Today, attrac-tive parks and promenades line the shores, apicturesque scene especially as the sun goesdown over the water. At Fener and Balat,neighbourhoods midway up the Golden Horn,

there are entire streets filled with old wooden houses, churches, and synagoguesdating from Byzantine and Ottoman times. The Orthodox Patriarchy resides at

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Fener and a little further up the Golden Horn at Eyup, are some wonderful ex-amples of Ottoman architecture. Muslim pilgrims from all over the world visitEyup Camii and Tomb of Eyup, the Prophet Mohammed’s standard bearer, andit is one of the holiest places in Islam. The area is still a popular burial place,and the hills above the mosque are dotted with modern gravestones interspersedwith ornate Ottoman stones. The Pierre Loti Cafe, atop the hill overlooking theshrine and the Golden Horn, is a wonderful place to enjoy the tranquility of theview.

Beyoglu and Taksim: Beyoglu is an interesting example of a district with European-influenced architecture, from a century before. Europe’s second oldest subway,Tunel was built by the French in 1875, must be also one of the shortest offeringa one-stop ride to start of Taksim. Near to Tunel is the Galata district, whoseGalata Tower became a famous symbols of Istanbul, and the top of which offersa tremendous 180 degree view of the city.

From the Tunel area to Taksim square isone of the city’s focal points for shopping, en-tertainment and urban promenading: IstiklalCadesi is a fine example of the contrasts andcompositions of Istanbul; fashion shops, book-shops, cinemas, markets, restaurants and evenhand-carts selling trinkets and simit (sesamebread snack) ensure that the street is packed throughout the day until late intothe night. The old tramcars re-entered into service, which shuttle up and downthis fascinating street, and otherwise the street is entirely pedestrianised. Thereare old embassy buildings, Galatasaray High School, the colourful ambience ofBalık Pazarı (Fish Bazaar) and restaurants in Cicek Pasajı (Flower Passage). Alsoon this street is the oldest church in the area, St. Mary’s Draperis dating back to1789, and the Franciscan Church of St. Antoine, demolished and then rebuilt in1913.

The street ends at Taksim Square, a huge open plaza, the hub of modern Is-tanbul and always crowded, crowned with an imposing monument celebratingAtaturk and the War of Independence. The main terminal of the new subway isunder the square, adjacent is a noisy bus terminal, and at the north end is theAtaturk Cultural Centre, one of the venues of the Istanbul Theatre Festival. Sev-eral five-star hotels are dotted around this area, like the Hyatt, Intercontinentaland Hilton (the oldest of its kind in the city). North of the square is the IstanbulMilitary Museum.

Taksim and Beyoglu have for centuries been the centre of nightlife, and nowthere are many lively bars and clubs off Istiklal Cadesi, including some of theonly gay venues in the city. Beyoglu is also the centre of the more bohemian artsscene.

Sultanahmet: Many places of tourist interest are concentrated in Sultanahmet,heart of the Imperial Centre of the Ottoman Empire. The most important placesin this area, all of which are described in detail in the Places of Interest section,

198

are Topkapı Palace, Aya Sofia, Sultan Ahmet Camii (the Blue Mosque), the Hip-podrome, Kapalı Carsı (Covered Market), Yerebatan Sarnıcı and the Museum ofIslamic Art.

In addition to this wonderful selection ofhistorical and architectural sites, Sultanahmetalso has a large concentration of carpet andsouvenir shops, hotels and guesthouses, cafes,bars and restaurants, and travel agents.Ortakoy: Ortakoy was a resort for the Ot-toman rulers because of its attractive locationon the Bosporus, and is still a popular spot forresidents and visitors. The village is within a

triangle of a mosque, church and synagogue, and is near Cıragan Palace, KabatasHigh School, Feriye, Princess Hotel.

The name Ortakoy reflects the university students and teachers who wouldgather to drink tea and discuss life, when it was just a small fishing village. Thesedays, however, that scene has developed into a suburb with an increasing amountof expensive restaurants, bars, shops and a huge market. The fishing, however,lives on and the area is popular with local anglers, and there is now a huge wa-terfront tea-house which is crammed at weekends and holidays.Sarıyer: The first sight of Sarıyer is where the Bosporus connects with the BlackSea, after the bend in the river after Tarabya. Around this area, old summerhouses, embassies and fish restaurants line the river, and a narrow road whichseparates it from Buyukdere, continues along to the beaches of Kilyos.

Sariyer and Rumeli Kavagı are the final wharfs along the European side vis-ited by the Bosporus boat trips. Both these districts, famous for their fish restau-rants along with Anadolu Kavagı, get very crowded at weekends and holidayswith Istanbul residents escaping the city.

After these points, the Bosporus is lined with tree-covered cliffs and littlehabitation. The Sadberk Hanım Museum, just before Sarıyer, is an interestingplace to visit; a collection of archaeological and ethnographic items, housed intwo wooden houses. A few kilometres away is the huge Belgrade Forest, once ahaunting ground of the Ottomans, and now a popular weekend retreat into thelargest forest area in the city.Uskudar: Relatively unknown to tourists, thesuburb of Uskudar, on the Asian side of theBosporus, is one of the most attractive suburbs.Religiously conservative in its background, ithas a tranquil atmosphere and some fine ex-amples of imperial and domestic architecture.The Iskele, or Mihrimah Camii is opposite themain ferry pier, on a high platform with a hugecovered porch in front, often occupied by olderlocal men watching life around them. Opposite this is Yeni Valide Camii, built in

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1710, and the Valide Sultan’s green tomb rather like a giant birdcage. The CiniliMosque takes its name from the beautiful tiles which decorate the interior, andwas built in 1640.

Apart from places of religious interest, Uskudar is also well known as a shop-ping area, with old market streets selling traditional local produce, and a goodfleamarket with second hand furniture. There are plenty of good restaurants andcafes with great views of the Bosporus and the rest of the city, along the quayside.In the direction of Haydarpasa is the lhe Karaca Ahmet Cemetery, the largestMuslim graveyard in Istanbul. The front of the Camlıca hills lie at the ridge ofarea and also offer great panoramic views of the islands and river.Kadıkoy: Further south along the Bosporus towards the Sea of Marmara, Kadıkoyhas developed into a lively area with up-market shopping, eating and entertain-ment making it popular especially with wealthy locals. Once prominent in thehistory of Christianity, the 5th century hosted important consul meetings here,but there are few reminders of that age. It is one of the improved districts ofIstanbul over the last century, and fashionable area to promenade along the wa-terfront in the evenings, especially around the marinas and yacht clubs.

Bagdat Caddesi is one of the most trendy and label-conscious fashion shop-ping streets, and for more down-to-earth goods, the Gen Azım Gunduz Caddesiis the best place for clothes, and the bit pazarı on Ozelellik Sokak is good forbrowsing through junk. In the district of Moda is the Benadam art gallery, as wellas many foreign cuisine restaurants and cafes.Haydarpasa: To the north of Kadıkoy is Haydarpasa, and the train station builtin 1908 with Prussain-style architecture which was the first stop along the Bagh-dad railway. Now it is the main station going to eastbound destinations bothwithin Turkey, and internationally. There are tombs and monuments dedicatedto the English and French soldiers who lost their lives during the Crimean War(1854–56), near the military hospital. The north-west wing of the 19th CenturySelimiye Barracks once housed the hospital, used by Florence Nightingale to carefor soldiers, and remains to honour her memory.Polonezkoy: Polonezkoy, although still within the city, is 25 km away from thecentre and not easy to reach by public transport. Translated as village of thePoles, the village has a fascinating history: It was established in 1848 by PrinceCzartorisky, leader of the Polish nationals who was granted exile in the OttomanEmpire to escape oppression in the Balkans. During his exile, he succeeded inestablishing a community of Balkans, which still survives, on the plot of landsold to him by a local monastery.

Since the 1970s the village has become a popular place with local Istanbu-lites, who buy their pig meat there (pig being forbidden under Islamic law andtherefore difficult to get elsewhere). All the Poles have since left the village, andthe place is inhabited now by wealthy city people, living in the few remainingCentral European style wooden houses with pretty balconies.

What attracts most visitors to Polonezkoy is its vast green expanse, whichwas designated Istanbul’s first national park, and the walks though forests with

200

streams and wooden bridges. Because of its popularity, it gets crowded at week-ends and the hotels are usually full.

Kilyos: Kilyos is the nearest beach resort to the city, on the Black Sea coast on theEuropean side of the Bosporus. Once a Greek fishing village, it has quickly beendeveloped as a holiday-home development, and gets very crowded in summer.Because of its ease to get there, 25 km and plenty of public transport, it is good fora day trip, and is a popular weekend getaway with plenty of hotels, and a coupleof campsites.

Sile: A pleasant, small holiday town, Sile lies 50 km from Uskudar on the BlackSea coast and some people even live here and commute into Istanbul. The whitesandy beaches are easily accessible from the main highway, lying on the west,as well as a series of small beaches at the east end. The town itself if perchedon a clifftop over looking the bay tiny island. There is an interesting French-built black-and-white striped lighthouse, and 14th century Genoese castle on thenearby island. Apart from its popular beaches, the town is also famous for itscraft; Sile bezi, a white muslin fabric a little like cheesecloth, which the localwomen embroider and sell their products on the street, as well as all over Turkey.

The town has plenty of accommodation available, hotels, guest houses andpansiyons, although can get very crowded at weekends and holidays as it is verypopular with people from Istanbul for a getaway, especially in the summer. Thereare small restaurants and bars in the town.

Prince’s Islands: Also known as Istanbul Islands, there are eight within one hourfrom the city, in the Marmara Sea. Boats ply the islands from Sirkeci, Kabatasand Bostancı, with more services during the summer. These islands, on whichmonasteries were established during the Byzantine period, were a popular sum-mer retreat for palace officials. It is still a popular escape from the city, withwealthier owning summer houses.

The largest and most popular is Buyukada(the Great Island). Large wooden man-sions still remain from the 19th century whenwealthy Greek and Armenian bankers builtthem as holiday villas. The island has alwaysbeen a place predominantly inhabited by mi-norities, hence Islam has never had a strongpresence here. Buyukada has long had a his-tory of people coming here in exile or retreat;its most famous guest being Leon Trotsky, who stayed for four years writing ‘TheHistory of the Russian Revolution’. The monastery of St. George also played hostto the granddaughter of Empress Irene, and the royal princess Zoe, in 1012. Theisland consists of two hills, both surmounted by monasteries, with a valley be-tween. Motor vehicles are banned, so getting around the island can be done bygraceful horse and carriage, leaving from the main square off Isa Celebi Sokak.Bicycles can also be hired. The southern hill, Yule Tepe, is the quieter of the twoand also home of St. George’s Monastery. It consists of a series of chapels on three

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levels, the site of which is a building dating back to the 12th century. In Byzan-tine times it was used as an asylum, with iron rings on the church floors used torestrain patients. On the northern hill is the monastery Isa Tepe, a 19th centuryhouse. The entire island is lively and colourful, with many restaurants, hotels,tea houses and shops. There are huge well-kept houses, trim gardens, and pinegroves, as well as plenty of beach and picnic areas.

Smaller and less of a tourist infrastructure is Burgazada. The famous Turkishnovelist, Sait Faik Abasiyanik lived here, and his house has been turned into amuseum dedicated to his work, and retains a remarkable tranquil and hallowedatmosphere.

Heybeliada, ‘Island of the Saddlebag’, be-cause of its shape, is loved for its naturalbeauty and beaches. It also has a highlyprestigious and fashionable watersports clubin the northwest of the island. One of itsbest-known landmarks is the Greek OrthodoxSchool of Theology, with an important collec-tion of Byzantine manuscripts. The school sitsloftily on the northern hill, but permission is

needed to enter, from the Greek Orthodox Patriarchate in Fener. The Deniz HarpOkulu, the Naval High School, is on the east side of the waterfront near the jetty,which was originally the Naval War Academy set up in 1852, then a high schoolsince 1985. Walking and cycling are popular here, plus isolated beaches as wellas the public Yoruk Beach, set in a magnificent bay. There are plenty of goodlocal restaurants and tea houses, especially along Ayyıldız Caddesi, and the at-mosphere is one of a close community.

Environment: Wide beaches of Kilyos at European side of Black Sea at 25th kmoutside Istanbul, are attracting Istanbul residents during summer months. Bel-grade Forest, inside from Black Sea, at European Side is the widest forest aroundIstanbul. Istanbul residents, at weekends, come here for family picnic with bra-zier at its shadows. 7 old water tank and some natural resources in the regioncompose a different atmosphere. Moglova Aqueduct, which is constructed byMimar Sinan during 16th century among Ottoman aqueducts, is the greatest one.800 m long Sultan Suleyman Aqueduct, which is passing over Golf Club, and alsoa piece of art of Mimar Sinan is one of the longest aqueducts within Turkey.

Polonezkoy, which is 25 km away from Istanbul, is founded at Asia coastduring 19th century by Polish immigrants. Polonezkoy, for walking in villageatmosphere, travels by horse, and tasting traditional Polish meals served by rel-atives of initial settlers, is the resort point of Istanbul residents. Beaches, restau-rants and hotels of Sile at Black Sea coast and 70 km away from Uskudar, areturning this place into one of the most cute holiday places of Istanbul. Regionwhich is popular in connection with tourism, is the place where famous Sile clothis produced.

Bayramoglu - Darica Bird Paradise and Botanic Park is a unique resort place

202

38 km away from Istanbul. This gargantuan park with its trekking roads, restau-rants is full of bird species and plants, coming from various parts of the world.

Sweet Eskihisar fisherman borough, towhose marina can be anchored by yachtsmenafter daily voyages in Marmara Sea is at southeast of Istanbul. Turkey’s 19th century famouspainter, Osman Hamdi Bey’s house in boroughis turned into a museum. Hannibal’s tomb be-tween Eskihisar and Gebze is one of the sitesaround a Byzantium castle.

There are lots of Istanbul residents’ sum-mer houses in popular holiday place 65 km away from Istanbul, Silivri. This is ahuge holiday place with magnificent restaurants, sports and health centers. Con-ference center is also attracting businessmen, who are escaping rapid tempo ofurban life for “cultural tourism” and business - holiday mixed activities. Sched-uled sea bus service is connecting Istanbul to Silivri.

Islands within Marmara Sea, which is adorned with nine islands, was thebanishing place of the Byzantium princes. Today they are now wealthy Istanbulresidents’ escaping places for cool winds during summer months and 19th cen-tury smart houses. The biggest one of the islands is Buyukada. You can have amarvelous phaeton travel between pine trees or have a swim within one of thenumerous bays around islands!

Other popular islands are Kınali, Sedef, Burgaz and Heybeliada. Regularferry voyages are connecting islands to both Europe and Asia coasts. There is arapid sea bus service from Kabatas during summers.

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Useful Information

Airport

Istanbul has two airports, the major Ataturk International Airport on the Euro-pean shore of the Sea of Marmara and Sabiha Gokcen Airport on the east sideof the Bosporus. Most long-haul international flights to Turkey land at AtaturkInternational Airport (IST) 23 km (14 miles) west of the city center at Yesilkoy.ICDEA08 Staff will meet you at the exit gate of Ataturk International AirportTerminal and help your transfer. The modern International Terminal (Dis Hat-lar Terminali) is spacious and efficient, with all the expected services includingATMs (cash machines) from which you can obtain New Turkish Liras, currencyexchange offices, restaurants, cafes, shops, Emanet (Baggage Check, Left Lug-gage). An underground passage (15-minute walk) connects the International Ter-minal with the older Domestic Terminal (Ic Hatlar Terminali) and also the Istan-bul Metro, called the Hafif Metro (”Light rail system”) on airport terminal signs.You can board a Metro train right from the airport and ride to Zeytinburnu, whereyou can transfer to the Zeytinburnu-Besiktas tram for the ride to SultanahmetSquare, Sirkeci Station, the Eminonu ferry and Sea Bus docks, the Galata Bridge,Karakoy and its ferry docks, and the Kabatas ferry docks and Funikuler to Tak-sim Square. A faster way to Taksim Square is by express city bus 96T, stoppingat Yenikapi, Aksaray and Taksim. A taxi from the airport to Sultanahmet costsabout US$18 to $25; to Taksim Square, about US$21 to $26; add 50% if you travelbetween 24:00 (midnight) and 06:00 am. The trip takes between 35 and 75 min-utes, depending on traffic. Havas airport buses, long the mainstay of airport-citytransfers, are being phased out. Traditionally, they departed the Arrivals level ofboth the International and Domestic terminals. The trip to Taksim takes between45 and 65 minutes, depending upon traffic.

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Passport and visa

Most of the travelers to Turkey require a visa. For most of them visas can beobtained at the port of entry in Turkey or from the Turkish Consulate Generalor Turkish Diplomatic Missions of their home countries. Sticker type visas areissued at the port of entry and allow staying in Turkey for up to 90 days. It isadvisable to have a minimum of six months validity on your passport from thedate of your entry into Turkey.

Banking and currency

The currency of Turkey is New Turkish Lira (YTL) as of 1 January 2005. 1YTLequals to 100 New Kurus (YKR) Banknotes come in 1YTL, 5YTL, 10YTL, 20YTL,50YTL & 100YTL and coins come in 1, 5YKR, 10YKR, 25YKR and 50YKR and1YTL. Currency exchange facilities are available in all banks, hotels and airports.24 hour cash machines providing banking services by different banks are locatedat suitable points throughout the 3 terminals of Antalya Airport. US dollars andEuros are also widely accepted. Credit cards are accepted at most restaurants andshops, the most widely used being MasterCard & Visa. Please kindly note thatAmerican Express, Diners Club and JCB Cards are not commonly accepted.

Business hours

Banks are generally open from 09:30–16:00 hours Monday–Friday. General officehours are 09:00–17:00 Monday–Friday. Post offices operate within these hours,however stamps are often available from hotels.

Electricity

Turkey operates on 220 volts, 50 Hz, with round-prong European-style plugs thatfit into recessed wall sockets/points. Check your appliances before leaving hometo see what you’ll need to plug in when you travel in Turkey. Many appliancessuch as laptop computers and digital cameras with their own power adapterscan be plugged into either 120-volt or 220-volt sockets/points and will adapt to

206

the voltage automatically. But you will need a plug adaptor that can fit into therecessed wall socket/point. Read the technical stuff on your power adapter tosee “INPUT: A.C. 100-240V”. If it reads that way, it can operate on either 120 or220 voltage. If it says something like “INPUT: 100-125V”, then it can’t run onTurkey’s 220 volts and you’ll need to bring a voltage converter.

Shopping

Shops are usually open between 8:30–19:00 and usually closed on Sunday. Turkey,as a result of its geographical location, is a treasure-house of hand-made products.These range from carpets and kilims, to gold and silver jewelry, ceramics, leatherand suede clothing, ornaments fashioned from alabaster, onyx, copper, and meer-schaum. When purchasing carpets, jewellery or leather products, it is advisableto consult your guide or do your shopping at a reputable store rather than in thestreet from vendors.

Tax refund

All goods and services in Turkey are applicable to 18% Value Added Tax. Youcan receive a tax refund for the goods you purchased in Turkey. Refunds willbe made to travelers who do not reside in Turkey. All goods are included inthe refunds with the exclusion of services rendered and the minimum amount ofpurchase that qualifies for refund is 5YTL. Retailers that qualify for tax refundsmust be “AUTHORIZED FOR REFUND”. These retailers must display a permitreceived from their respective tax office. The retailer will make four copies ofthe receipt for your refund, three of which will be received by the purchaser.If photocopies of the receipt are received the retailer must sign and stamp thecopies to validate them. If you prefer the refund to be made by check, a Tax-freeShopping Check for the amount to be refunded to the customer must be givenalong with the receipt. For the purchaser to benefit from this exemption he mustleave the country within three months with the goods purchased showing themto Turkish customs officials along with the appropriate receipts and or check.There are four ways to receive your refund:

1. If the retailer gives you a check, it can he cashed at a bank in the customsarea at the airport.

207

2. If customer sends a copy of the receipt to the retailer showing that the goodshave left the country within one month, the retailer will send a bank transferto the purchaser’s bank or credit card within ten days upon receiving thereceipt.

3. If the certified receipt and check are brought back to the retailer on a sub-sequent visit thin one-month of the date of customs certification, the refundcan be made directly to the purchaser.

4. The refund may be made by the organization of those companies that areauthorized to make tax refunds.

Geography

The summer months in Istanbul are generally hot and quite humid. The winterscan be cold and wet, although not as extreme as other areas of the country. Thesea temperature is creep up to 30 degrees in June, July and August, with verylittle rain. Spring and autumn are popular times to visit because of the comfort-able climate, good for lots of walking and sightseeing, with highs between 15–25degrees C, in April, May, September and October. By the winter, the dry cold airmass from the Black Sea and cold damp front from the Balkans brings a chillyseason with daytime highs of between 10–15 degrees C, and nights much colder.Although rarely falling to freezing point, there is the occasional light snow in thecity.

208

Index and E-mail Addresses

209

A

Abdeljawad, Thabet (Turkey), [email protected]

158Abderraman, Jesus (Spain), [email protected]

21, 22, 54Adıvar, Murat (Turkey), [email protected]

17, 18, 25, 55Adıyaman, Meltem (Turkey), [email protected]

158Afshar Kermani, Mozhdeh (Iran), mog [email protected]

29, 30, 56Agarwal, Ravi (USA), [email protected]

15, 16, 31, 36Aghazadeh, Nasser (Iran), [email protected]

17, 18, 57Akın-Bohner, Elvan (USA), [email protected]

19, 20, 31, 37Akman, Murat (Turkey), [email protected]

158Albayrak, Incı (Turkey), [email protected]

17, 18, 58Aldea Mendes, Diana (Portugal), [email protected]

17, 18, 59Alseda, Lluıs (Spain), [email protected]

17, 19, 20, 31, 38Al-Sharawi, Ziyad (Oman), [email protected]

25, 26, 60Altunkaynak, Meltem (Turkey), [email protected]

159Alzabut, Jehad (Turkey), [email protected]

25, 26, 61Appleby, John (Ireland), [email protected]

17, 21, 22, 62Aseeri, Samar (Saudi Arabia), [email protected]

29, 30, 63Atasever, Nurıye (Turkey), atasever [email protected]

210

17, 18, 64Atay, Fatıhcan M. (Germany), [email protected]

29, 30, 65Atıcı, Ferhan (USA), [email protected]

21, 22, 66Awerbuch Friedlander, Tamara (USA), [email protected]

17, 18, 25, 67Aydın, Kemal (Turkey), [email protected]

159Aydın, M. Aslı (Turkey), [email protected]

182

B

Bas, Mujgan (Turkey), [email protected]

159Batıt, Ozlem (Turkey), [email protected]

29, 30, 68Bayat, Kemal (Turkey), [email protected]

182Bernhardt, Chris (USA), [email protected]

17, 18, 69Bodine, Sigrun (USA), [email protected]

17, 25, 26, 70Bohner, Martin (USA), [email protected]

3, 5, 11, 15, 160, 185Bolat, Yasar (Turkey), [email protected]

29, 30, 71Bozok, Ilknur (Turkey), kuzu [email protected]

160Budakcı, Gulter (Turkey), [email protected]

160

C

Cakmak, Devrım (Turkey), [email protected]

25, 26, 72Camouzis, Elias (Greece), [email protected]

17, 21, 22, 73

211

Can, Canan (Turkey), canan can [email protected]

161Canovas, Jose S. (Spain), [email protected]

17, 18, 74Caylak, Duygu (Turkey), duygu [email protected]

161Celebi, Okay (Turkey), [email protected]

3, 27, 161Celık, Cem (Turkey), [email protected]

162Celık Kızılkan, Gulnur (Turkey), [email protected]

162Cetın, Erbıl (Turkey), [email protected]

25, 26, 75Cıbıkdıken, Alı Osman (Turkey), [email protected]

21, 22, 76Cınar, Cengız (Turkey), [email protected]

162Costa, Sara (Spain), [email protected]

17, 18, 77Cushing, J. M. (USA), [email protected]

11, 23, 25, 26, 78

D

Dagyar, Nazlı Ceren (Turkey), [email protected]

182Dannan, Fozi (Syria), [email protected]

25, 26, 79Das, Sebahat Ebru (Turkey), [email protected]

163Denız, Aslı (Turkey), [email protected]

163Dong, Zhaoyang (Spain), [email protected]

163Dosla, Zuzana (Czech Republic), [email protected]

5, 19, 25, 26, 80, 185

212

Dosly, Ondrej (Czech Republic), [email protected]

27, 28, 31, 39Duman, Ahmet (Turkey), [email protected]

21, 22, 81Duman, Melda (Turkey), [email protected]

164

E

Elaydi, Saber (USA), [email protected]

5, 9, 11, 164Emul, Yakup (Turkey), [email protected]

183Erbe, Lynn (USA), [email protected]

17, 18, 21, 82Erkal, Durdane (Turkey), [email protected]

183Erol, Meltem (Turkey), [email protected]

29, 30, 83Esty, Norah (USA), [email protected]

17, 18, 25, 84

F

Fernandes, Sara (Portugal), [email protected]

21, 22, 85

G

Gesztesy, Fritz (USA), [email protected]

19, 20, 23, 31, 40Getimane, Mario (Mozambique), [email protected]

164Gomes, Orlando (Portugal), [email protected]

17, 18, 86Gumus, Ibrahım Halıl (Turkey), [email protected]

165Gumus, Ozlem Ak (Turkey), [email protected]

25, 26, 87

213

Gurses, Metin (Turkey), [email protected]

5Guseinov, Gusein (Turkey), [email protected]

5, 25, 26, 88Guvenılır, A. Feza (Turkey), [email protected]

29, 30, 89Guzowska, Małgorzata (Poland), [email protected]

25, 26, 90Gyori, Istvan (Hungary), [email protected]

11, 15, 16, 31, 41

H

Hashemiparast, Moghtada (Iran), [email protected]

17, 18, 91Hatıpoglu, Veysel Fuat (Turkey), [email protected]

165Heim, Julius (USA), [email protected]

21, 22, 92Hilger, Stefan (Germany), [email protected]

15, 16, 25, 32, 42Hilscher, Roman (Czech Republic), [email protected]

15, 17, 18, 93

I

Intepe, Gokce (Turkey), [email protected]

165

J

Jantarakhajorn, Khajee (Thailand), [email protected]

166Jimenez Lopez, Vıctor (Spain), [email protected]

17, 18, 94

K

Kalabusic, Senada (Bosnia/Herz.), [email protected]

17, 18, 95

214

Karahan, Gokce (Turkey), [email protected]

183

Karakelle, Musa (Turkey), [email protected]

184

Kara, Rukıye (Turkey), [email protected]

166

Karpuz, Basak (Turkey), [email protected]

25, 26, 96

Kayar, Zeynep (Turkey), [email protected]

166

Kaymakcalan, Bıllur (USA), [email protected]

5, 15, 167

Keller, Christian (USA), [email protected]

21, 22, 97

Kent, Candace (USA), [email protected]

17, 21, 22, 98

Kharkov, Vitaliy (Ukraine), kharkov v [email protected]

25, 26, 99

Kipnis, Mikhail (Russia), [email protected]

25, 26, 100

Kıyak Ucar, Yelız (Turkey), [email protected]

167

Kloeden, Peter (Germany), [email protected]

5, 27, 28, 32, 43

Kocak, Huseyin (USA), [email protected]

19, 20, 32, 44

Kongnuan, Supachara (Thailand), [email protected]

167

Kosareva, Natalia (Russia), [email protected]

168

Kostrov, Yevgeniy (USA), [email protected]

21, 22, 101

Kratz, Werner (Germany), [email protected]

6

Kulik, Tomasia (Australia), [email protected]

21, 22, 102

215

Kulik, Yakov (Australia), [email protected]

168Kutay, Vıldan (Turkey), vildan [email protected]

168

L

Ladas, Gerasimos (USA), [email protected]

3, 12, 15, 27, 28, 32, 45, 185Laitochova, Jitka (Czech Republic), [email protected]

21, 22, 29, 103Lawrence, Bonita (USA), [email protected]

21–23, 104Leonhardt, Andreas (Germany), [email protected]

169Lesaja, Goran (USA), [email protected]

169Luıs, Rafael (Portugal), [email protected]

25, 26, 105Lutz, Donald (USA), [email protected]

6

M

Marsh, Robert L. (USA), [email protected]

169Matthews, Thomas (USA), [email protected]

21, 22, 106Mawhin, Jean (Belgium), [email protected]

6, 23, 24, 32, 46McCarthy, Michael (Ireland), [email protected]

21, 22, 107Mendes, Vivaldo (Portugal), [email protected]

17, 18, 21, 108Mert, Razıye (Turkey), [email protected]

25, 26, 109Mesgarani, Hamid (Iran), [email protected]

29, 30, 110

216

Michor, Johanna (USA), [email protected]

25, 29, 30, 111Migda, Małgorzata (Poland), [email protected]

29, 30, 112Mısır, Adıl (Turkey), [email protected]

170Morales, Leopoldo (Spain), [email protected]

21, 22, 113

N

Nishimura, Kazuo (Japan), [email protected]

7Nurkanovic, Mehmed (Bosnia/Herz.), [email protected]

170Nurkanovic, Zehra (Bosnia/Herz.), [email protected]

170

O

Oban, Volkan (Turkey), [email protected]

17, 18, 114Oberste-Vorth, Ralph (USA), [email protected]

17, 18, 115Ocalan, Ozkan (Turkey), [email protected]

29, 171Okumus, Israfıl (Turkey), [email protected]

171Oliveira, Henrique (Portugal), [email protected]

7, 21, 22, 116O’Regan, Donal (Ireland), [email protected]

6Ozdemır, Huseyın (Turkey), [email protected]

184Ozen, Bahadır (Turkey), [email protected]

184Ozkan, Umut Mutlu (Turkey), umut [email protected]

171

217

Ozpınar, Fıgen (Turkey), [email protected]

172Ozturk, Rukıye (Turkey), [email protected]

25, 26, 117Ozturk, Sermın (Turkey), [email protected]

172Ozugurlu, Ersın (Turkey), [email protected]

172

P

Papaschinopoulos, Garyfalos (Greece), [email protected]

17, 18, 118Park, Choonkil (South Korea), [email protected]

25, 26, 119Peterson, Allan (USA), [email protected]

6, 12, 15, 16, 19, 32, 47Pinelas, Sandra (Portugal), [email protected]

17, 18, 21, 120Pituk, Mihaly (Hungary), [email protected]

25, 26, 29, 121Popescu, Emil (Romania), [email protected]

123Popescu, Nedelia Antonia (Romania), [email protected]

17, 29, 30, 124Pop, Nicolae (Romania), [email protected]

17, 18, 122Pospısil, Zdenek (Czech Republic), [email protected]

25, 26, 125Potzsche, Christian (Germany), [email protected]

19, 21, 22, 126Predescu, Mihaela (USA), [email protected]

17, 18, 21, 127

R

Rabbani, Mohsen (Iran), [email protected]

29, 30, 128

218

Rachidi, Mustapha (France), [email protected]

21, 22, 129Radin, Michael (USA), [email protected]

21, 22, 130Rasmussen, Martin (Germany), [email protected]

21, 22, 131Reankittiwat, Paramee (Thailand), [email protected]

173Rehak, Pavel (Czech Republic), [email protected]

25, 26, 132Reinfelds, Andrejs (Latvia), [email protected]

21, 22, 25, 133Rodkina, Alexandra (Jamaica), [email protected]

21, 22, 134Romero i Sanchez, David (Spain), [email protected]

29, 30, 135Ruffing, Andreas (Germany), [email protected]

7, 12, 173

S

Sacker, Robert J. (USA), [email protected]

7, 12Saker, Samir (Saudi Arabia), [email protected]

136Sanchez-Moreno, Pablo (Spain), [email protected]

29, 30, 137Savun, Ipek (Turkey), ipek [email protected]

173Schinas, Christos (Greece), [email protected]

17, 18, 138Schmeidel, Ewa (Poland), [email protected]

29, 30, 139Sekercı, Nurcan (Turkey), [email protected]

21, 22, 140Sell, George (USA), [email protected]

11

219

Selmanogulları, Tugcen (Turkey), [email protected]

174Seneetantikul, Soporn (Thailand), [email protected]

174Seyhan, Gızem (Turkey), [email protected]

174Shahrezaee, Mohsen (Iran), [email protected]

17, 18, 141Sharkovsky, Alexander (Ukraine), [email protected]

6Siddikov, Bakhodirzhon (USA), [email protected]

17, 18, 29, 142Simon, Moritz (Germany), [email protected]

25, 26, 143Sımsek, Dagıstan (Turkey), [email protected]

175Sırma, Alı (Turkey), [email protected]

29, 30, 144Sizer, Walter (USA), [email protected]

175Smith, Hal (USA), [email protected]

23, 24, 33, 48Stefanidou, Gesthimani (Greece), [email protected]

21, 22, 145Stehlik, Petr (Czech Republic), [email protected]

17, 18, 146Suhrer, Andreas (Germany), [email protected]

175

T

Taskara, Necatı (Turkey), [email protected]

176Teschl, Gerald (Austria), [email protected]

6, 19, 25, 26, 147Thongjub, Nawalax (Thailand), [email protected]

176

220

Tıryakı, Aydın (Turkey), [email protected]

3, 25, 26, 148Tlemcani, Mouhaydine (Portugal), [email protected]

21, 22, 149Tollu, D. Turgut (Turkey), hasan [email protected]

176Topal, Fatma Serap (Turkey), [email protected]

29, 30, 150

U

Ucar, Denız (Turkey), [email protected]

177Unal, Mehmet (Turkey), [email protected]

1, 3, 177, 185

V

Vanderbauwhede, Andre (Belgium), [email protected]

19, 20, 33, 49Vesarachasart, Sirichan (Thailand), [email protected]

177Vu, Dominik (Austria), [email protected]

178

Y

Yalazlar, Gulcın (Turkey), sugulu [email protected]

178Yalcınkaya, Ibrahım (Turkey), [email protected]

178Yantır, Ahmet (Turkey), [email protected]

17, 18, 151Yıgıder, Muhammed (Turkey), m.yigider [email protected]

179Yıldırım, Ahmet (Turkey), [email protected]

29, 30, 152Yıldız, Mustafa Kemal (Turkey), [email protected]

179

221

Yılmaz, Ozlem (Turkey), [email protected]

179Yorke, James A. (USA), [email protected]

23, 24, 33, 50Yoruk, Fulya (Turkey), fulya [email protected]

180

Z

Zafer, Agacık (Turkey), [email protected]

3, 23, 24, 29, 33, 51, 185Zaidi, Atiya (Australia), [email protected]

21, 22, 153Zakeri, Ali (Iran), [email protected]

29, 30, 154Zeidan, Vera (USA), [email protected]

15–17, 33, 52Zemanek, Petr (Czech Republic), [email protected]

29, 30, 155

222

decoupling and simplifying of discrete dynamical systems in the

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