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Exploring chaos: theory and experiment

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Bibliographic Details
Main Author:	Davies, Brian (Author)
Format:	Book
Language:	English
Published:	Reading, Mass. Perseus Books 1999
Edition:	1. print.
Series:	Studies in nonlinearity
Subjects:	Chaos Chaos (théorie des systèmes) Dynamique différentiable Chaotic behavior in systems Differentiable dynamical systems Dynamisches System Chaostheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	XIII, 237 S. graph. Darst.
ISBN:	0738200905

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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
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discipline	Informatik Mathematik
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isbn	0738200905
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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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