A first course in chaotic dynamical systems: theory and experiment
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. u. a.
Addison-Wesley
1992
|
| Edition: | 1. print. |
| Series: | Studies in nonlinearity
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 302 S. Ill., graph. Darst. |
| ISBN: | 0201554062 |
Staff View
MARC
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| 245 | 1 | 0 | |a A first course in chaotic dynamical systems |b theory and experiment |c Robert L. Devaney |
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| 264 | 1 | |a Reading, Mass. u. a. |b Addison-Wesley |c 1992 | |
| 300 | |a XI, 302 S. |b Ill., graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Studies in nonlinearity | |
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Record in the Search Index
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| adam_text | CONTENTS ix
Contents
Chapter 1. A Mathematical and Historical Tour 1
1.1 Images from Dynamical Systems 1
1.2 A Brief History of Dynamics 5
Chapter 2. Examples of Dynamical Systems 9
2.1 An Example from Finance 9
2.2 An Example from Ecology 11
2.3 Finding Roots and Solving Equations 12
2.4 Differential Equations 15
: Chapter 3. Orbits 17
3.1 Iteration 17
3.2 Orbits 18
3.3 Types of Orbits 19
3.4 Other Orbits 22
| 3.5 The Doubling Function 24
I 3.6 Experiment: The Computer May Lie 25
Chapter 4. Graphical Analysis 29
I 4.1 Graphical Analysis 29
! 4.2 Orbit Analysis 32
4.3 The Phase Portrait 33
Chapter 5. Fixed and Periodic Points 36
5.1 A Fixed Point Theorem 36
5.2 Attraction and Repulsion 37
5.3 Calculus of Fixed Points 38
5.4 Why Is This True? 42
5.5 Periodic Points 46
5.6 Experiment: Rates of Convergence 48
I
x DYNAMICAL SYSTEMS
Chapter 6. Bifurcations 52 |
i
6.1 Dynamics of the Quadratic Map 52
6.2 The Saddle Node Bifurcation 57
6.3 The Period Doubling Bifurcation 61
6.4 Experiment: The Transition to Chaos 63 .
Chapter 7. The Quadratic Family 69
7.1 The Case c = 2 69
7.2 The Case c 2 71
7.3 The Cantor Middle Thirds Set 75
Chapter 8. Transition to Chaos 82
8.1 The Orbit Diagram 82
8.2 The Period Doubling Route to Chaos 89
8.3 Experiment: Windows in the Orbit Diagram 92
Chapter 9. Symbolic Dynamics 97
9.1 Itineraries 97
9.2 The Sequence Space 98
9.3 The Shift Map 103
9.4 Conjugacy 106
Chapter 10. Chaos 114
10.1 Three Properties of a Chaotic System 114
10.2 Other Chaotic Systems 121
10.3 Manifestations of Chaos 126
10.4 Experiment: Feigenbaum s Constant 128
Chapter 11. Sarkovskii s Theorem 133
11.1 Period 3 Implies Chaos 133
11.2 Sarkovskii s Theorem 137
11.3 The Period 3 Window 142
11.4 Subshifts of Finite Type 146
Chapter 12. The Role of the Critical Orbit 154
12.1 The Schwarzian Derivative 154
12.2 The Critical Point and Basins of Attraction 157
Chapter 13. Newton s Method 164
13.1 Basic Properties 164
13.2 Convergence and Nonconvergence 169
Chapter 14. Fractals 176
14.1 The Chaos Game 176
CONTENTS xi
14.2 The Cantor Set Revisited 178
14.3 The Sierpinski Triangle 180
14.4 The Koch Snowflake 182
14.5 Topological Dimension 185
14.6 Fractal Dimension 186
14.7 Iterated Function Systems 190
14.8 Experiment: Iterated Function Systems 197
Chapter 15. Complex Functions 203
15.1 Complex Arithmetic 203
15.2 Complex Square Roots 207
15.3 Linear Complex Functions 209
15.4 Calculus of Complex Functions 212
Chapter 16. The Julia Set 221
16.1 The Squaring Function 221
16.2 The Chaotic Quadratic Function 226
16.3 Cantor Sets Again 227
16.4 Computing the Filled Julia Set 233
16.5 Experiment: Filled Julia Sets and Critical Orbits 238
16.6 The Julia Set as a Repellor 239
Chapter 17. The Mandelbrot Set 246
17.1 The Fundamental Dichotomy 246
17.2 The Mandelbrot Set 249
17.3 Experiment: Periods of Other Bulbs 253
17.4 Experiment: Periods of the Decorations 257
17.5 Experiment: Find the Julia Set 258
17.6 Experiment: Spokes and Antennae 259
17.7 Experiment: Similarity of the Mandelbrot and Julia Sets 260
Chapter 18. Further Projects and Experiments 263
18.1 The Tricorn 263
18.2 Cubics 264
18.3 Exponential Functions 267
18.4 Trigonometric Functions 270
18.5 Complex Newton s Method 273
Appendix A. Mathematical Preliminaries 279
Appendix B. Algorithms 287
Appendix C. References 295
Index 299
|
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| indexdate | 2024-07-09T17:17:23Z |
| institution | BVB |
| isbn | 0201554062 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005458723 |
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| physical | XI, 302 S. Ill., graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
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| publisher | Addison-Wesley |
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| series2 | Studies in nonlinearity |
| spelling | Devaney, Robert L. Verfasser aut A first course in chaotic dynamical systems theory and experiment Robert L. Devaney 1. print. Reading, Mass. u. a. Addison-Wesley 1992 XI, 302 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in nonlinearity Sistemas Dinamicos larpcal Chaotic behavior in systems Differentiable dynamical systems Chaos (DE-588)4191419-3 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s Dynamisches System (DE-588)4013396-5 s DE-604 Differenzierbares dynamisches System (DE-588)4137931-7 s Chaos (DE-588)4191419-3 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005458723&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Devaney, Robert L. A first course in chaotic dynamical systems theory and experiment Sistemas Dinamicos larpcal Chaotic behavior in systems Differentiable dynamical systems Chaos (DE-588)4191419-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Dynamisches System (DE-588)4013396-5 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4191419-3 (DE-588)4137931-7 (DE-588)4013396-5 (DE-588)4316104-2 |
| title | A first course in chaotic dynamical systems theory and experiment |
| title_auth | A first course in chaotic dynamical systems theory and experiment |
| title_exact_search | A first course in chaotic dynamical systems theory and experiment |
| title_full | A first course in chaotic dynamical systems theory and experiment Robert L. Devaney |
| title_fullStr | A first course in chaotic dynamical systems theory and experiment Robert L. Devaney |
| title_full_unstemmed | A first course in chaotic dynamical systems theory and experiment Robert L. Devaney |
| title_short | A first course in chaotic dynamical systems |
| title_sort | a first course in chaotic dynamical systems theory and experiment |
| title_sub | theory and experiment |
| topic | Sistemas Dinamicos larpcal Chaotic behavior in systems Differentiable dynamical systems Chaos (DE-588)4191419-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Dynamisches System (DE-588)4013396-5 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Sistemas Dinamicos Chaotic behavior in systems Differentiable dynamical systems Chaos Differenzierbares dynamisches System Dynamisches System Chaotisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005458723&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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