Synopses & Reviews
This is the only book that introduces the full range of activity in the rapidly growing field of nonlinear dynamics to an audience of students, scientists, and engineers with no in-depth experience in the area. The text uses a step-by-step explanation of dynamics and geometry in state space as a foundation for understanding nonlinear dynamics. It goes on to provide a thorough treatment of such key topics as differential equation models and iterated map models (including a derivation of the famous Feigenbaum numbers), the surprising role of number theory in dynamics, and an introduction to Hamiltonian dynamics. This is the only book written at this introductory level to include the increasingly important field of pattern formation, along with a survey of the controversial questions of quantum chaos. Important analytical tools, such as Lyapunov exponents, Kolmogorov entropies, and fractal dimensions, are treated in detail. With over 200 figures and diagrams, and both analytic and computer exercises following every chapter, the book is ideally suited for use as a text or for self-instruction. An extensive collection of annotated references brings the reader into contact with the literature in nonlinear dynamics, which the reader will be prepared to tackle after completing the book.
Synopsis
This book introduces readers to the full range of current and background activity in the rapidly growing field of nonlinear dynamics. It uses a step-by-step introduction to dynamics and geometry in state space to help in understanding nonlinear dynamics and includes a thorough treatment of both differential equation models and iterated map models as well as a derivation of the famous Feigenbaum numbers. It is the only introductory book available that includes the important field of pattern formation and a survey of the controversial questions of quantum chaos. This second edition has been restructured for easier use and the extensive annotated references are updated through January 2000 and include many web sites for a number of the major nonlinear dynamics research centers. With over 200 figures and diagrams, analytic and computer exercises this book is a necessity for both the classroom and the lab.
Description
Includes bibliographical references (p. 605-642) and index.
Table of Contents
First Edition Preface
First Edition Acknowledgments
Second Edition Preface
Second Edition Acknowledgments
I. The Phenomenology of Chaos
1. Three Chaotic Systems
2. The Universality of Chaos
II. Toward a Theory of Nonlinear Dynamics and Chaos
3. Dynamics in State Space: One and Two Dimensions
4. Three-Dimensional State Space and Chaos
5. Iterated Maps
6. Quasi-Periodicity and Chaos
7. Intermittency and Crises
8. Hamiltonian Systems
III. Measures of Chaos
9. Quantifying Chaos
10. Many Dimensions and Multifractals
IV. Special Topics
11. Pattern Formation and Spatiotemporal Chaos
12. Quantum Chaos, The Theory of Complexity, and Other Topics
Appendix A: Fourier Power Spectra
Appendix B: Bifurcation Theory
Appendix C: The Lorenz Model
Appendix D: The Research Literature on Chaos
Appendix E: Computer Programs
Appendix F: Theory of the Universal Feigenbaum Numbers
Appendix G: The Duffing Double-Well Oscillator
Appendix H: Other Universal Feature for One-Dimensional Iterated Maps
Appendix I: The van der Pol Oscillator
Appendix J: Simple Laser Dynamics Models
References
Index