Verfügbarkeit: Chaos :: THWS Bibkatalog

Chaos: a program collection for the PC ; with many numerical experiments

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Bibliographische Detailangaben
Hauptverfasser:	Korsch, Hans-Jürgen 1944- (VerfasserIn), Jodl, Hans-Jörg (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin [u.a.] Springer 1999
Ausgabe:	2. ed.
Schlagworte:	Computersimulation Chaostheorie Simulation Chaotisches System Personal Computer Nichtlineares dynamisches System Software Einführung
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	CD-ROM für Windows 95 und NT
Beschreibung:	XV, 311 S. Ill., graph. Darst. CD-ROM (12 cm)
ISBN:	3540638938

Internformat

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Datensatz im Suchindex

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adam_text	Table of Contents 1 Overview and Basic Concepts 1 1.1 Introduction 1 1.2 The Programs 5 1.3 Literature on Chaotic Dynamics 8 2 Nonlinear Dynamics and Deterministic Chaos 11 2.1 Deterministic Chaos 11 2.2 Hamiltonian Systems 12 2.2.1 Integrable and Ergodic Systems 13 2.2.2 Poincare Sections 16 2.2.3 The KAM Theorem 18 2.2.4 Homoclinic Points 20 2.3 Dissipative Dynamical Systems 21 2.3.1 Attractors 23 2.3.2 Routes to Chaos 25 2.4 Special Topics 27 2.4.1 The Poincare Birkhoff Theorem 27 2.4.2 Continued Fractions 29 2.4.3 The Lyapunov Exponent 31 2.4.4 Fixed Points of One Dimensional Maps 34 2.4.5 Fixed Points of Two Dimensional Maps 37 2.4.6 Bifurcations 42 References 43 3 Billiard Systems 45 3.1 Deformations of a Circle Billiard 47 3.2 Numerical Techniques 51 3.3 Interacting with the Program 52 3.4 Computer Experiments 56 3.4.1 From Regularity to Chaos 56 3.4.2 Zooming In 58 3.4.3 Sensitivity and Determinism 60 3.4.4 Suggestions for Additional Experiments 61 Stability of Two Bounce Orbits 61 XII Table of Contents Bifurcations of Periodic Orbits 62 A New Integrable Billiard? 64 Non Convex Billiards 64 3.5 Suggestions for Further Studies 64 3.6 Real Experiments and Empirical Evidence 65 References 65 4 Gravitational Billiards: The Wedge 67 4.1 The Poincare Mapping 68 4.2 Interacting with the Program 73 4.3 Computer Experiments 75 4.3.1 Periodic Motion and Phase Space Organization 75 4.3.2 Bifurcation Phenomena 80 4.3.3 Plane Filling Wedge Billiards 84 4.3.4 Suggestions for Additional Experiments 86 Mixed A B Orbits 86 Pure B Dynamics 87 The Stochastic Region 87 Breathing Chaos 87 4.4 Suggestions for Further Studies 87 4.5 Real Experiments and Empirical Evidence 88 References 88 5 The Double Pendulum 89 5.1 Equations of Motion 89 5.2 Numerical Algorithms 91 5.3 Interacting with the Program 93 5.4 Computer Experiments 98 5.4.1 Different Types of Motion 98 5.4.2 Dynamics of the Double Pendulum 103 5.4.3 Destruction of Invariant Curves 107 5.4.4 Suggestions for Additional Experiments 110 Testing the Numerical Integration 110 Zooming In 110 Different Pendulum Parameters Ill 5.5 Real Experiments and Empirical Evidence 112 References 114 6 Chaotic Scattering 115 6.1 Scattering off Three Disks 117 6.2 Numerical Techniques 121 6.3 Interacting with the Program . 122 6.4 Computer Experiments 124 6.4.1 Scattering Functions and Two Disk Collisions 124 6.4.2 Tree Organization of Three Disk Collisions 127 6.4.3 Unstable Periodic Orbits 129 Table of Contents XIII 6.4.4 Fractal Singularity Structure 131 6.4.5 Suggestions for Additional Experiments 133 Long Lived Trajectories 133 Incomplete Symbolic Dynamics 135 Multiscale Fractals 135 6.5 Suggestions for Further Studies 135 6.6 Real Experiments and Empirical Evidence 135 References 136 7 Fermi Acceleration 137 7.1 Fermi Mapping 138 7.2 Interacting with the Program 139 7.3 Computer Experiments 141 7.3.1 Exploring Phase Space for Different Wall Oscillations . . 141 7.3.2 KAM Curves and Stochastic Acceleration 144 7.3.3 Fixed Points and Linear Stability 147 7.3.4 Absolute Barriers 148 7.3.5 Suggestions for Additional Experiments 150 Higher Order Fixed Points 150 Standard Mapping 151 Bifurcation Phenomena 152 Influence of Different Wall Velocities 153 7.4 Suggestions for Further Studies 154 7.5 Real Experiments and Empirical Evidence 155 References 155 8 The Duffing Oscillator 157 8.1 The Duffing Equation 157 8.2 Numerical Techniques 161 8.3 Interacting with the Program 161 8.4 Computer Experiments 165 8.4.1 Chaotic and Regular Oscillations 165 8.4.2 The Free Duffing Oscillator 166 8.4.3 Anharmonic Vibrations: Resonances and Bistability . . . 166 8.4.4 Coexisting Limit Cycles and Strange Attractors 170 8.4.5 Suggestions for Additional Experiments 173 Harmonic Oscillator 173 Gravitational Pendulum 174 Exact Harmonic Response 174 Period Doubling Bifurcations 175 Strange Attractors 177 8.5 Suggestions for Further Studies 177 8.6 Real Experiments and Empirical Evidence 178 References 179
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author	Korsch, Hans-Jürgen 1944- Jodl, Hans-Jörg
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spellingShingle	Korsch, Hans-Jürgen 1944- Jodl, Hans-Jörg Chaos a program collection for the PC ; with many numerical experiments Computersimulation (DE-588)4148259-1 gnd Chaostheorie (DE-588)4009754-7 gnd Simulation (DE-588)4055072-2 gnd Chaotisches System (DE-588)4316104-2 gnd Personal Computer (DE-588)4115533-6 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd
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title	Chaos a program collection for the PC ; with many numerical experiments
title_auth	Chaos a program collection for the PC ; with many numerical experiments
title_exact_search	Chaos a program collection for the PC ; with many numerical experiments
title_full	Chaos a program collection for the PC ; with many numerical experiments H. J. Korsch ; H.-J.Jodl
title_fullStr	Chaos a program collection for the PC ; with many numerical experiments H. J. Korsch ; H.-J.Jodl
title_full_unstemmed	Chaos a program collection for the PC ; with many numerical experiments H. J. Korsch ; H.-J.Jodl
title_short	Chaos
title_sort	chaos a program collection for the pc with many numerical experiments
title_sub	a program collection for the PC ; with many numerical experiments
topic	Computersimulation (DE-588)4148259-1 gnd Chaostheorie (DE-588)4009754-7 gnd Simulation (DE-588)4055072-2 gnd Chaotisches System (DE-588)4316104-2 gnd Personal Computer (DE-588)4115533-6 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd
topic_facet	Computersimulation Chaostheorie Simulation Chaotisches System Personal Computer Nichtlineares dynamisches System Software Einführung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008065223&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT korschhansjurgen chaosaprogramcollectionforthepcwithmanynumericalexperiments AT jodlhansjorg chaosaprogramcollectionforthepcwithmanynumericalexperiments

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