Chaos in dynamical systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Press
1993
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 385 S. graph. Darst. |
| ISBN: | 0521432154 0521437997 |
Internformat
MARC
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| 100 | 1 | |a Ott, Edward |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Chaos in dynamical systems |c Edward Ott |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS PREFACE XI 1 INTRODUCTION AND OVERVIEW 1 1.1 SOME HISTORY 1 1.2
EXAMPLES OF CHAOTIC BEHAVIOR 2 1.3 DYNAMICAL SYSTEMS 6 1.4 ATTRACTORS 10
1.5 SENSITIVE DEPENDENCE ON INITIAL CONDITIONS 15 1.6 DELAY COORDINATES
19 PROBLEMS 21 NOTES 22 2 ONE-DIMENSIONAL MAPS 23 2.1 PIECEWISE LINEAR
ONE-DIMENSIONAL MAPS 23 2.2 THE LOGISTIC MAP 31 2.3 GENERAL DISCUSSION
OF SMOOTH ONE-DIMENSIONAL MAPS 44 2.4 EXAMPLES OF APPLICATIONS OF
ONE-DIMENSIONAL MAPS TO CHAOTIC SYSTEMS OF HIGHER DIMENSIONALITY 56
APPENDIX: SOME ELEMENTARY DEFINITIONS AND THEOREMS CONCERNING SETS 64
PROBLEMS 66 NOTES 68 3 STRANGE ATTRACTORS AND FRACTAL DIMENSION 69 3.1
THE BOX-COUNTING DIMENSION 69 3.2 THE GENERALIZED BAKER S MAP 75 3.3
MEASURE AND THE SPECTRUM OF D Q DIMENSIONS 78 3.4 DIMENSION SPECTRUM FOR
THE GENERALIZED BAKER S MAP 81 3.5 CHARACTER OF THE NATURAL MEASURE FOR
THE GENERALIZED BAKER S MAP 83 3.6 THE POINTWISE DIMENSION 86 3.7
IMPLICATIONS AND DETERMINATION OF FRACTAL DIMENSION IN EXPERIMENTS 89
3.8 EMBEDDING 93 3.9 FAT FRACTALS 97 APPENDIX: HAUSDORFF DIMENSION 100
PROBLEMS 103 NOTES 106 4 DYNAMICAL PROPERTIES OF CHAOTIC SYSTEMS 108 4.1
THE HORSESHOE MAP AND SYMBOLIC DYNAMICS 108 4.2 LINEAR STABILITY OF
STEADY STATES AND PERIODIC ORBITS 115 4.3 STABLE AND UNSTABLE MANIFOLDS
122 4.4 LYAPUNOV EXPONENTS 129 4.5 ENTROPIES 138 4.6 CONTROLLING CHAOS
145 APPENDIX: GRAM-SCHMIDT ORTHOGONALIZATION 148 PROBLEMS 148 NOTES 150
5 NONATTRACTING CHAOTIC SETS 151 5.1 FRACTAL BASIN BOUNDARIES 152 5.2
FINAL STATE SENSITIVITY 158 5.3 STRUCTURE OF FRACTAL BASIN BOUNDARIES
161 5.4 CHAOTIC SCATTERING 166 5.5 THE DYNAMICS OF CHAOTIC SCATTERING
170 5.6 THE DIMENSIONS OF NONATTRACTING CHAOTIC SETS AND THEIR STABLE
AND UNSTABLE MANIFOLDS 176 APPENDIX: DERIVATION OF EQS. (5.3) 179
PROBLEMS 181 NOTES 183 6 QUASIPERIODICITY 184 6.1 FREQUENCY SPECTRUM AND
ATTRACTORS 184 6.2 THE CIRCLE MAP 190 6.3 N FREQUENCY QUASIPERIODICITY
WITH N 2 200 6.4 STRANGE NONCHAOTIC ATTRACTORS OF QUASIPERIODICALLY
FORCED SYSTEMS 205 PROBLEMS 206 NOTES 206 7 CHAOS IN HAMILTONIAN SYSTEMS
208 7.1 HAMILTONIAN SYSTEMS 208 7.2 PERTURBATION OF INTEGRABLE SYSTEMS
224 7.3 CHAOS AND KAM TORI IN SYSTEMS DESCRIBABLE BY TWO-DIMENSIONAL
HAMILTONIAN MAPS 235 7.4 HIGHER-DIMENSIONAL SYSTEMS 255 7.5 STRONGLY
CHAOTIC SYSTEMS 257 7.6 THE SUCCESSION OF INCREASINGLY RANDOM SYSTEMS
261 PROBLEMS 262 NOTES 264 8 CHAOTIC TRANSITIONS 266 8.1 THE PERIOD
DOUBLING CASCADE ROUTE TO CHAOTIC ATTRACTORS 267 8.2 THE INTERMITTENCY
TRANSITION TO A CHAOTIC ATTRACTOR 272 8.3 CRISES 277 8.4 THE LORENZ
SYSTEM: AN EXAMPLE OF THE CREATION OF A CHAOTIC TRANSIENT 291 8.5 BASIN
BOUNDARY METAMORPHOSES 294 8.6 BIFURCATIONS TO CHAOTIC SCATTERING 299
PROBLEMS 303 NOTES 304 9 MULTIFRACTALS 305 9.1 THE SINGULARITY SPECTRUM
F(A) 305 9.2 THE PARTITION FUNCTION FORMALISM 313 9.3 LYAPUNOV PARTITION
FUNCTIONS 316 9.4 DISTRIBUTION OF FINITE TIME LYAPUNOV EXPONENTS 322 9.5
UNSTABLE PERIODIC ORBITS AND THE NATURAL MEASURE 326 9.6 VALIDITY OF THE
LYAPUNOV AND PERIODIC ORBITS PARTITION FUNCTIONS FOR NONHYPERBOLIC
ATTRACTORS 330 PROBLEMS 332 NOTES 332 10 QUANTUM CHAOS 334 10.1 THE
ENERGY LEVEL SPECTRA OF CHAOTIC, BOUNDED, TIME-INDEPENDENT SYSTEMS 336
10.2 WAVEFUNCTIONS FOR CLASSICALLY CHAOTIC, BOUNDED, TIME-INDEPENDENT
SYSTEMS 352 10.3 TEMPORALLY PERIODIC SYSTEMS 354 10.4 QUANTUM CHAOTIC
SCATTERING 360 PROBLEMS 361 NOTES 361 REFERENCES 363 INDEX 382
|
| any_adam_object | 1 |
| author | Ott, Edward |
| author_facet | Ott, Edward |
| author_role | aut |
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| callnumber-first | Q - Science |
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| callnumber-search | Q172.5.C45 |
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| callnumber-subject | Q - General Science |
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| ctrlnum | (OCoLC)27432580 (DE-599)BVBBV008047495 |
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| dewey-ones | 003 - Systems |
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| dewey-tens | 000 - Computer science, information, general works |
| discipline | Physik Informatik Mathematik |
| edition | 1. publ. |
| format | Book |
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| indexdate | 2024-07-09T17:13:28Z |
| institution | BVB |
| isbn | 0521432154 0521437997 |
| language | English |
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| physical | XII, 385 S. graph. Darst. |
| publishDate | 1993 |
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| spelling | Ott, Edward Verfasser aut Chaos in dynamical systems Edward Ott 1. publ. Cambridge u.a. Cambridge Univ. Press 1993 XII, 385 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chaos Chaos - Problèmes et exercices Chaos gtt Dynamische systemen gtt Fisica Geral larpcal Chaotic behavior in systems Chaotisches System (DE-588)4316104-2 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s Dynamisches System (DE-588)4013396-5 s DE-604 Chaostheorie (DE-588)4009754-7 s 1\p DE-604 OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005295076&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ott, Edward Chaos in dynamical systems Chaos Chaos - Problèmes et exercices Chaos gtt Dynamische systemen gtt Fisica Geral larpcal Chaotic behavior in systems Chaotisches System (DE-588)4316104-2 gnd Chaostheorie (DE-588)4009754-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4316104-2 (DE-588)4009754-7 (DE-588)4013396-5 |
| title | Chaos in dynamical systems |
| title_auth | Chaos in dynamical systems |
| title_exact_search | Chaos in dynamical systems |
| title_full | Chaos in dynamical systems Edward Ott |
| title_fullStr | Chaos in dynamical systems Edward Ott |
| title_full_unstemmed | Chaos in dynamical systems Edward Ott |
| title_short | Chaos in dynamical systems |
| title_sort | chaos in dynamical systems |
| topic | Chaos Chaos - Problèmes et exercices Chaos gtt Dynamische systemen gtt Fisica Geral larpcal Chaotic behavior in systems Chaotisches System (DE-588)4316104-2 gnd Chaostheorie (DE-588)4009754-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Chaos Chaos - Problèmes et exercices Dynamische systemen Fisica Geral Chaotic behavior in systems Chaotisches System Chaostheorie Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005295076&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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