Chaotic Dynamics: An Introduction

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ISBN: 9780521476850 | 0521476852
Cover: Paperback
Copyright: 1/26/1996

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This new edition of Chaotic Dynamics can be used as a text for a unit on chaos for physics and engineering students at the second- and third-year level. Such a unit would fit very well into modern physics and classical mechanics courses.

Preface

Acknowledgments

xiv

Introduction

(6)

Some helpful tools

(32)

Phase space

(14)

Poincare section

(6)

Spectral analysis of time series

(12)

Problems

(4)

Visualization of the pendulum's dynamics

(35)

Sensitivity to initial conditions

(2)

Phase diagrams and Poincare sections

(16)

Time series and power spectra

(1)

Basins of attraction

(7)

Bifurcation diagrams

(8)

Problems and simulations

(2)

Toward an understanding of chaos

(35)

The logistic map

(13)

Period doubling

(4)

The periodic windows

(3)

Lyapunov exponents

(2)

Entropy

(2)

Stretching and folding

(1)

The circle map

(7)

The horseshoe map

(4)

Application to the pendulum

100

(9)

Problems

105

(4)

The characterization of chaotic attractors

109

(24)

Dimension

110

(9)

Lyapunov exponents

119

(4)

Lyapunov exponents and dimension

123

(3)

Information change and Lyapunov exponents

126

(7)

Problems

129

(4)

Experimental characterization, prediction, and modification of chaotic states

133

(33)

Characterization of chaotic states

133

(19)

Experiment and simulation

135

(2)

Reconstruction of the attractor

137

(2)

Time-delay coordinates

139

(4)

Choosing the time delay

143

(2)

Embedding dimension and attractor dimension

145

(5)

Lyapunov exponents

150

(2)

Summary

152

(1)

Prediction of chaotic states

152

(7)

Method of analogues

153

(3)

Linear approximation method

156

(3)

Modification of chaotic states

159

(4)

Conclusion

163

(3)

Problems

164

(2)

Chaos broadly applied

166

(24)

Chaos in lasers

166

(2)

Chaotic chemical reactions

168

(2)

Chaos in fluid dynamics

170

(2)

Spatio-temporal chaos in fluids

172

(6)

Spatio-temporal chaos in thermal convection

173

(3)

Spatio-temporal chaos on a rotating fluid film

176

(2)

Spatio-temporal intermittency in model equations

178

(1)

Strong turbulence

179

(1)

Chaotic mixing in fluids

180

(1)

Complex dynamics of interfacial growth: artificial snowflakes

181

(3)

Chaos in earthquake dynamics

184

(1)

Chaos and quantum physics

185

(2)

Foundations of statistical mechanics

187

(2)

Conclusion

189

(1)

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Chaotic Dynamics: An Introduction

Summary

Table of Contents

Supplemental Materials