Chaotic Dynamics: An Introduction

by Gregory L. Baker , Jerry P. Gollub

• ISBN13: 9780521476850
• ISBN10: 0521476852
• Edition: 2nd
• Format: Paperback
• Copyright: 1996-01-26
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface	xi
Acknowledgments	xiv
Introduction	1	(6)
Some helpful tools	7	(32)
Phase space	7	(14)
Poincare section	21	(6)
Spectral analysis of time series	27	(12)
Problems	35	(4)
Visualization of the pendulum's dynamics	39	(35)
Sensitivity to initial conditions	41	(2)
Phase diagrams and Poincare sections	43	(16)
Time series and power spectra	59	(1)
Basins of attraction	59	(7)
Bifurcation diagrams	66	(8)
Problems and simulations	72	(2)
Toward an understanding of chaos	74	(35)
The logistic map	76	(13)
Period doubling	77	(4)
The periodic windows	81	(3)
Lyapunov exponents	84	(2)
Entropy	86	(2)
Stretching and folding	88	(1)
The circle map	89	(7)
The horseshoe map	96	(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)
Further reading	190	(3)
Appendix A Numerical integration - Runge-Kutta method	193	(3)
Appendix B Computer program listings	196	(46)
Appendix C Solutions to selected problems	242	(4)
References	246	(7)
Index	253	(3)
Diskette order information	256