
- 118 pages
- English
- PDF
- Available on iOS & Android
Survey Of Nonlinear Dynamics ("Chaos Theory")
About this book
This book is intended to give a survey of the whole field of nonlinear dynamics (or "chaos theory") in compressed form. It covers quite a range of topics besides the standard ones, for example, pde dynamics and Galerkin approximations, critical phenomena and renormalization group approach to critical exponents. The many meanings or measures of "chaos" in the literature are summarized. A precise definition of chaos based on a carefully limited sensitive dependence is offered. An application to quantum chaos is made. The treatment does not emphasize mathematical rigor but insists that the crucial concepts and theorems be mathematically well-defined. Thus topology plays a basic role. This alone makes this book unique among short surveys, where the inquisitive reader must usually be satisfied with colorful similes, analogies, and hand-waving arguments.Richard Ingraham graduated with B.S. summa cum laude in mathematics from Harvard college and with M.A. and Ph.D in Physics from Harvard Graduate School. He was granted the Sheldon Prize Traveling Fellowship by Harvard College and was a member of the Institute for Advanced Study at Princeton for two years.
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Table of contents
- CONTENTS
- PREFACE
- 1. INTRODUCTORY REMARKS
- 2. FUNDAMENTALS OF CONTINUOUS TIME SYSTEMS
- 3. DISCRETE TIME SYSTEMS: ITERATION OF MAPS
- 4. HAMILTONIAN SYSTEMS
- 5. MEASURES OF CHAOS
- 6. RENORMALIZATION GROUP
- 7. PARTIAL DIFFERENTIAL EQUATIONS
- 8. EXPERIMENTAL REALIZATIONS OF NONLINEAR DYNAMICS
- REFERENCES
- APPENDIX A GENERAL LINEAR STABILITY ANALYSIS
- APPENDIX B PROOF OF NO SENSITIVE DEPENDENCE IN THE QUANTUM-MECHANICAL SELF-CORRELATION
- GLOSSARY OF PRINCIPAL TERMS
- INDEX