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.
- 124 pages
- English
- PDF
- Available on iOS & Android
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Survey Of Nonlinear Dynamics ("Chaos Theory")
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Topic
Physical SciencesSubtopic
Chaotic Behavior in SystemsTable 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
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Yes, you can access Survey Of Nonlinear Dynamics ("Chaos Theory") by Richard L Ingraham in PDF and/or ePUB format, as well as other popular books in Physical Sciences & Chaotic Behavior in Systems. We have over 1.5 million books available in our catalogue for you to explore.