A Survey of Nonlinear Dynamics: "chaos Theory"

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World Scientific, 1992 - Science - 107 pages
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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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Contents

PREFACE v
1
ITERATION OF MAPS
21
Vlll
23
HAMILTONIAN SYSTEMS
39
MEASURES OF CHAOS
55
RENORMALIZATION GROUP
65
PARTIAL DIFFERENTIAL EQUATIONS
79
EXPERIMENTAL REALIZATIONS OF NONLINEAR DYNAMICS
89
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