Exploring chaos: theory and experiment
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass.
Perseus Books
1999
|
| Ausgabe: | 1. print. |
| Schriftenreihe: | Studies in nonlinearity
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 237 S. graph. Darst. |
| ISBN: | 0738200905 |
Internformat
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| 100 | 1 | |a Davies, Brian |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Exploring chaos |b theory and experiment |c Brian Davies |
| 250 | |a 1. print. | ||
| 264 | 1 | |a Reading, Mass. |b Perseus Books |c 1999 | |
| 300 | |a XIII, 237 S. |b graph. Darst. | ||
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| 490 | 0 | |a Studies in nonlinearity | |
| 650 | 4 | |a Chaos | |
| 650 | 7 | |a Chaos (théorie des systèmes) |2 ram | |
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Datensatz im Suchindex
| _version_ | 1804128123285929984 |
|---|---|
| adam_text | EXPLORING CHAOS THEORY AND EXPERIMENT BRIAN DAVIES THE ADVANCED BOOK
PROGRAM PERSEUS BOOKS READING, MASSACHUSETTS CONTENTS INTRODUCTION 1 1.1
DYNAMICAL MODELS 1 1.2 CELESTIAL MECHANICS . 5 1.3 LORENZ: THE END OF
WEATHER PREDICTION? 7 1.4 COMPLEX BEHAVIOUR OF SIMPLE SYSTEMS 11 ORBITS
OF ONE-DIMENSIONAL SYSTEMS 13 2.1 DISCRETE DYNAMICAL SYSTEMS 13 2.2
FIXED POINTS AND STABILITY 19 2.3 SOME ORBITS OF THE TENT MAP 24 2.4
PERIOD DOUBLING OF THE LOGISTIC MAP 30 2.5 PERIODIC ORBITS AND
COMPOSITIONS 34 2.6 THE FULLY CHAOTIC TENT MAP 37 2.7 NUMERICAL VERSUS
EXACT ORBITS 41 2.8 FOURIER ANALYSIS OF AN ORBIT 44 2.9 LYAPUNOV
EXPONENT OF AN ORBIT 51 2.10 CHAOTIC ORBITS . 55 2.11 ERGODIC ORBITS 60
BIFURCATIONS IN ONE-DIMENSIONAL SYSTEMS 65 3.1 BIFURCATION DIAGRAMS . .
. . 65 3.2 FINAL STATE DIAGRAMS 67 3.3 PERIOD DOUBLING MECHANISM 71
3.4 PERIOD DOUBLING CASCADES 79 3.5 FEIGENBAUM S UNIVERSAL CONSTANTS 82
3.6 TANGENT BIFURCATIONS 89 3.7 INTERMITTENT BEHAVIOUR 92 3.8 UNSTABLE
ORBITS AND CRISES 96 3.9 TRANSCRITICAL AND PITCHFORK BIFURCATIONS 100
3.10 THEORY OF FEIGENBAUM SCALING 103 TWO-DIMENSIONAL SYSTEMS 107 4.1
THE HENON MAP 107 4.2 FIXED POINTS 113 XI XII CONTENTS 4.3 AREA
CONTRACTION 116 4.4 STABILITY OF FIXED POINTS 119 4.5 LYAPUNOV EXPONENTS
.- 127 4.6 BASIN BOUNDARIES 132 4.7 RETURN MAPS 136 4.8 LINEAR FEEDBACK
AND CONTROL 140 4.9 PRODUCING THE STRANGE ATTRACTOR 145 5 FRACTALS 147
5.1 THE HENON ATTRACTOR 148 5.2 THE CANTOR SET 150 5.3 FRACTAL
BIFURCATION DIAGRAMS 155 5.4 CAPACITY DIMENSION 157 5.5 CAPACITY
DIMENSION OF THE HENON ATTRACTOR 161 5.6 SELF-SIMILAR FRACTALS 165 5.7
LYAPUNOV DIMENSION OF TWO-DIMENSIONAL MAPS 167 5.8 THE ROSSLER ATTRACTOR
170 5.9 THE FEIGENBAUM ATTRACTOR 172 6 NON-LINEAR OSCILLATIONS 177 6.1
THE DRIVEN NON-LINEAR PENDULUM 177 6.2 PHASE PLANE 182 6.3 POINCARE
SECTIONS . . 186 6.4 LYAPUNOV EXPONENTS 191 A CHAOS FOR JAVA SOFTWARE
197 A.I INSTALLATION 197 A.2 GENERAL FEATURES 198 A.3 BIFURCATION
DIAGRAMS . . 205 A.4 FOURIER ANALYSIS 206 A.5 GRAPHICAL ANALYSIS 207
A.6 ITERATE(ID) 209 A.7 ITERATE(2D) -.211 A.8 LYAPUNOV EXPONENTS 214 A.9
ODE ORBITS * 215 A.10 POINCARE SECTIONS 217 A.11 RETURN MAPS 218 B
DISCRETE FOURIER TRANSFORM 221 B.I COMPLEX ROOTS OF UNITY 221 B.2
DISCRETE ORTHOGONALITY 222 B.3 FOURIER AMPLITUDES 222 B.4 USING REAL AND
IMAGINARY PARTS 223 CONTENTS XIII B.5 FAST FOURIER TRANSFORM 224 C
VARIATIONAL EQUATIONS 225 C.I DERIVATION AND MEANING 225 C.2 THE AREA
CONTRACTING PROPERTY 225 C.3 THREE-DIMENSIONAL CASE 226 D LIST OF MAPS
AND DIFFERENTIAL EQUATIONS 227 D.I ONE-DIMENSIONAL MAPS 227 D.2
TWO-DIMENSIONAL MAPS 228 D.3 DIFFERENTIAL EQUATIONS 228 BIBLIOGRAPHY 229
INDEX 232
|
| any_adam_object | 1 |
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| classification_tum | MAT 587f |
| ctrlnum | (OCoLC)41972838 (DE-599)BVBBV013348409 |
| dewey-full | 003/.857 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003/.857 |
| dewey-search | 003/.857 |
| dewey-sort | 13 3857 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| edition | 1. print. |
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| indexdate | 2024-07-09T18:44:14Z |
| institution | BVB |
| isbn | 0738200905 |
| language | English |
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| physical | XIII, 237 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Perseus Books |
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| series2 | Studies in nonlinearity |
| spelling | Davies, Brian Verfasser aut Exploring chaos theory and experiment Brian Davies 1. print. Reading, Mass. Perseus Books 1999 XIII, 237 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in nonlinearity Chaos Chaos (théorie des systèmes) ram Dynamique différentiable Chaotic behavior in systems Differentiable dynamical systems Dynamisches System (DE-588)4013396-5 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Chaostheorie (DE-588)4009754-7 s 1\p DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009102974&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 | Davies, Brian Exploring chaos theory and experiment Chaos Chaos (théorie des systèmes) ram Dynamique différentiable Chaotic behavior in systems Differentiable dynamical systems Dynamisches System (DE-588)4013396-5 gnd Chaostheorie (DE-588)4009754-7 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4009754-7 |
| title | Exploring chaos theory and experiment |
| title_auth | Exploring chaos theory and experiment |
| title_exact_search | Exploring chaos theory and experiment |
| title_full | Exploring chaos theory and experiment Brian Davies |
| title_fullStr | Exploring chaos theory and experiment Brian Davies |
| title_full_unstemmed | Exploring chaos theory and experiment Brian Davies |
| title_short | Exploring chaos |
| title_sort | exploring chaos theory and experiment |
| title_sub | theory and experiment |
| topic | Chaos Chaos (théorie des systèmes) ram Dynamique différentiable Chaotic behavior in systems Differentiable dynamical systems Dynamisches System (DE-588)4013396-5 gnd Chaostheorie (DE-588)4009754-7 gnd |
| topic_facet | Chaos Chaos (théorie des systèmes) Dynamique différentiable Chaotic behavior in systems Differentiable dynamical systems Dynamisches System Chaostheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009102974&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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