Introduction to chaos and coherence:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Bristol u.a.
Inst. of Physics Publ.
1992
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 130, [4] S. Ill., zahlr. graph. Darst. |
| ISBN: | 0750301945 0750301953 |
Staff View
MARC
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| 100 | 1 | |a Frøyland, Jan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to chaos and coherence |c Jan Frøyland |
| 264 | 1 | |a Bristol u.a. |b Inst. of Physics Publ. |c 1992 | |
| 300 | |a X, 130, [4] S. |b Ill., zahlr. graph. Darst. | ||
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| 650 | 4 | |a Chaos déterministe | |
| 650 | 7 | |a Chaos |2 gtt | |
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Record in the Search Index
| _version_ | 1804119828731002880 |
|---|---|
| adam_text | CONTENTS
Preface ix
1 Introduction 1
2 Fractals 3
2.1 A Cantor set 4
2.2 The Koch triadic island 5
2.3 Fractal dimensions 7
3 The logistic map 9
3.1 The linear map 9
3.2 Definition of the logistic map. Scaling and translation
transformations 10
3.3 The fixed points and their stability 11
3.4 Period two 14
3.5 The period doubling route to chaos. Feigenbaum s
constants 15
3.6 Chaos and strange attractors 16
3.7 The critical point and its iterates 17
3.8 Self similarity, scaling and universality 19
3.9 Reversed bifurcations. Crisis 21
3.10 Lyapunov exponents 23
3.11 Statistical properties of chaotic orbits 26
3.12 Dimensions of attractors 27
3.13 Tangent bifurcations and intermittency 29
3.14 Exact results at A = 1 31
3.15 Predicted power spectra. Critical exponents. Effect of
noise 33
3.16 Experiments relevant to the logistic map 34
3.17 Poincare maps and return maps 35
3.18 Closing remarks on the logistic map 37
v
vi CONTENTS
4 The circle map 38
4.1 The fixed points 38
4.2 Circle maps near K = 0. Arnol d tongues 39
4.3 The critical value K = 1 42
4.4 Period two, bimodality, superstability and swallowtails 42
4.5 Where can there be chaos? 45
5 Higher dimensional maps 49
5.1 Linear maps in higher dimensions 49
5.2 Manifolds. Homoclinic and heteroclinic points 52
5.3 Lyapunov exponents in higher dimensional maps 54
5.4 The Kaplan Yorke conjecture 56
5.5 The Hopf bifurcation 57
6 Dissipative maps in higher dimensions 58
6.1 The Henon map 58
6.2 The complex logistic map 62
6.3 Two dimensional coupled logistic map 65
7 Conservative maps 80
7.1 The twist map 80
7.2 The KAM theorem 83
7.3 The rings of Saturn 83
8 Cellular automata 87
9 Ordinary differential equations 92
9.1 Fixed points. Linear stability analysis 94
9.2 Homoclinic and heteroclinic orbits 95
9.3 Lyapunov exponents for flows 97
9.4 Hopf bifurcations for flows 98
10 The Lorenz model 101
11 Time series analysis 107
11.1 Fractal dimension from a time series 107
11.2 Autoregressive models 109
11.3 Rescaled range analysis 113
11.4 The global temperature: an example 115
CONTENTS vii
Appendices 119
Al Period three in the logistic map 119
A2 Lyapunov exponents algorithm 122
A2.1 Lyapunov exponents for maps 122
A2.2 Lyapunov exponents for flows 123
A2.3 Practical hints 124
Further Reading 126
Index 128
|
| any_adam_object | 1 |
| author | Frøyland, Jan |
| author_facet | Frøyland, Jan |
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| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV005621788 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:32:24Z |
| institution | BVB |
| isbn | 0750301945 0750301953 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003519062 |
| oclc_num | 26634569 |
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| physical | X, 130, [4] S. Ill., zahlr. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Inst. of Physics Publ. |
| record_format | marc |
| spelling | Frøyland, Jan Verfasser aut Introduction to chaos and coherence Jan Frøyland Bristol u.a. Inst. of Physics Publ. 1992 X, 130, [4] S. Ill., zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chaos Chaos déterministe Chaos gtt Coherentie (natuurkunde) gtt Dynamique différentiable Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Chaos (DE-588)4191419-3 gnd rswk-swf Kohärenz (DE-588)4139923-7 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 s DE-604 Chaos (DE-588)4191419-3 s Kohärenz (DE-588)4139923-7 s Chaostheorie (DE-588)4009754-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003519062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Frøyland, Jan Introduction to chaos and coherence Chaos Chaos déterministe Chaos gtt Coherentie (natuurkunde) gtt Dynamique différentiable Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Chaos (DE-588)4191419-3 gnd Kohärenz (DE-588)4139923-7 gnd |
| subject_GND | (DE-588)4009754-7 (DE-588)4126142-2 (DE-588)4191419-3 (DE-588)4139923-7 |
| title | Introduction to chaos and coherence |
| title_auth | Introduction to chaos and coherence |
| title_exact_search | Introduction to chaos and coherence |
| title_full | Introduction to chaos and coherence Jan Frøyland |
| title_fullStr | Introduction to chaos and coherence Jan Frøyland |
| title_full_unstemmed | Introduction to chaos and coherence Jan Frøyland |
| title_short | Introduction to chaos and coherence |
| title_sort | introduction to chaos and coherence |
| topic | Chaos Chaos déterministe Chaos gtt Coherentie (natuurkunde) gtt Dynamique différentiable Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Chaos (DE-588)4191419-3 gnd Kohärenz (DE-588)4139923-7 gnd |
| topic_facet | Chaos Chaos déterministe Coherentie (natuurkunde) Dynamique différentiable Chaotic behavior in systems Chaostheorie Nichtlineares dynamisches System Kohärenz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003519062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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