Chaos in discrete dynamical systems: a visuell introduction in 2 dimensions
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer [u.a.]
1997
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXV, 246 S. Ill. CD-ROM (12 cm) |
| ISBN: | 0387943005 |
Internformat
MARC
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| 100 | 1 | |a Abraham, Ralph |d 1936- |e Verfasser |0 (DE-588)115444254 |4 aut | |
| 245 | 1 | 0 | |a Chaos in discrete dynamical systems |b a visuell introduction in 2 dimensions |c Ralph H. Abraham ; Laura Gardini ; Christian Mira |
| 264 | 1 | |a New York |b Springer [u.a.] |c 1997 | |
| 300 | |a XXV, 246 S. |b Ill. |e CD-ROM (12 cm) | ||
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| 338 | |b nc |2 rdacarrier | ||
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| 650 | 0 | 7 | |a Differenzierbares dynamisches System |0 (DE-588)4137931-7 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Mira, Christian |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804126036036681728 |
|---|---|
| adam_text | Foreword to the Project ix
Preface to the Book xi
About the Book Authors xv
Preface to the CD ROM xvi
About the CD ROM Authors xix
Preface to the Website xx
Acknowledgments xx
Contents of the CD ROM xxv
PART I BASIC CONCEPTS I
Chapter I Introduction 3
I. I Background 3
1.2 History 3
1.3 Plan of the book 4
1.4 Context 4
1.5 Basic concepts of iteration theory 6
1.6 The families of maps 7
1.7 Critical points and curves 9
Chapter 2 Basic concepts in ID II
2.1 Maps II
2.2 Multiplicities 12
2.3 Trajectories and orbits 14
2.4 Attractors, basins, and boundaries 22
2.5 Bifurcations 23
2.6 Exemplary bifurcations 23
Chapter 3 Basic concepts in 2D 29
3.1 Maps 29
3.2 Multiplicities and critical curves 29
3.3 An example 30
3.4 Trajectories and orbits 33
3.5 Attractors 36
3.6 Bifurcations 37
xxi
PART 2 EXEMPLARY BIFURCATION
SEQUENCES 39
Chapter 4 Absorbing Areas 41
4.1 Absorption concepts, ID 41
4.2 Absorption concepts, 2D 41
4.3 Exemplary bifurcation sequence 45
Chapter 5 Holes 59
5.1 Introduction 59
5.2 Exemplary bifurcation sequence 59
Chapter 6 Fractal Boundaries 85
6.1 Contact bifurcation concepts 85
6.2 Exemplary bifurcation sequence 97
Chapter 7 Chaotic Contact Bifurcations 117
7.1 Bifurcations in one dimension I 17
7.2 Bifurcations in two dimensions 133
7.3 Exemplary bifurcation sequence 137
Chapter 8 Conclusion 151
PART 3 APPENDICES 153
Appendix I Notations 155
A 1.1 Formal logic 155
A 1.2 Set theory 155
A1.3 Point set topology 155
Appendix 2 Topological Dynamics 157
A2.1 Trajectories and orbits 157
xxii CHAOS IN DISCRETE DYNAMICAL SYSTEMS
A2.2 Inverse images 158
A2.3 Fixed points 158
A2.4 Periodic trajectories 159
A2.5 Limit points 159
A2.6 Stable sets, attractors, and basins 159
A2.7 Unstable sets and repellors 160
A2.8 Chaotic attractors 160
Appendix 3 Critical Curves 161
A3.1 The zones 161
A3.2 Critical points via calculus 162
A3.3 Critical points via topology 163
A3.4 The critical curves 164
A3.5 Absorbing areas 164
Appendix 4 Synonyms 165
Appendix 5 History, Part I 167
A5.1 Early history 167
A5.2 Finite difference equations 168
A5.3 Functional equations 169
A5.4 Poincare 170
A5.5 Independent contemporaries of Poincare 172
A5.6 Birkhoff 173
A5.7 Denjoy 174
A5.8 The Russian school 174
A5.9 The Japanese school 176
A5.10 Conservative systems 176
A5.11 The American school 178
A5.12 Numerical methods and applied work 178
A5.13 Iteration theory 178
A5.I4 The methods of Liapunov 180
A5.15 Periodic solutions 180
A5.I6 Control theory 180
A5.I7 Other applications 181
A5.I8 Conclusion 181
A5.19 Historical Bibliography 182
CONTENTS xxiii
Appendix 6 History, Part 2 209
A6.1 Introduction 209
A6.2 G.D. Birkhoff 211
A6.3 Nonlinear oscillations from 1925 213
A6.4 The Mandelstham Andronov school 215
A6.5 The Bogoliubov (or Kiev) school 224
A6.6 Poincare s analyticity theorem 225
A6.7 Myrberg s contribution 227
A6.8 Conclusion 229
Appendix 7 Domains of the Figures 231
Bibliography 235
Frequently used references by code 235
Bibliography by author 236
Index 245
xxiv CHAOS IN DISCRETE DYNAMICAL SYSTEMS
|
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| id | DE-604.BV011513846 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:11:04Z |
| institution | BVB |
| isbn | 0387943005 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007749292 |
| oclc_num | 164810791 |
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| owner | DE-12 DE-29T DE-N2 DE-706 DE-473 DE-BY-UBG |
| owner_facet | DE-12 DE-29T DE-N2 DE-706 DE-473 DE-BY-UBG |
| physical | XXV, 246 S. Ill. CD-ROM (12 cm) |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer [u.a.] |
| record_format | marc |
| spelling | Abraham, Ralph 1936- Verfasser (DE-588)115444254 aut Chaos in discrete dynamical systems a visuell introduction in 2 dimensions Ralph H. Abraham ; Laura Gardini ; Christian Mira New York Springer [u.a.] 1997 XXV, 246 S. Ill. CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Chaotisches System (DE-588)4316104-2 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s DE-604 Chaotisches System (DE-588)4316104-2 s Gardini, Laura 1952- Verfasser (DE-588)115524134 aut Mira, Christian Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007749292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abraham, Ralph 1936- Gardini, Laura 1952- Mira, Christian Chaos in discrete dynamical systems a visuell introduction in 2 dimensions Chaotisches System (DE-588)4316104-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4316104-2 (DE-588)4137931-7 |
| title | Chaos in discrete dynamical systems a visuell introduction in 2 dimensions |
| title_auth | Chaos in discrete dynamical systems a visuell introduction in 2 dimensions |
| title_exact_search | Chaos in discrete dynamical systems a visuell introduction in 2 dimensions |
| title_full | Chaos in discrete dynamical systems a visuell introduction in 2 dimensions Ralph H. Abraham ; Laura Gardini ; Christian Mira |
| title_fullStr | Chaos in discrete dynamical systems a visuell introduction in 2 dimensions Ralph H. Abraham ; Laura Gardini ; Christian Mira |
| title_full_unstemmed | Chaos in discrete dynamical systems a visuell introduction in 2 dimensions Ralph H. Abraham ; Laura Gardini ; Christian Mira |
| title_short | Chaos in discrete dynamical systems |
| title_sort | chaos in discrete dynamical systems a visuell introduction in 2 dimensions |
| title_sub | a visuell introduction in 2 dimensions |
| topic | Chaotisches System (DE-588)4316104-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Chaotisches System Differenzierbares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007749292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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