Global Transversality, Resonance And Chaotic Dynamics

by Luo, Albert C. J.

• ISBN13: 9789812771117
• ISBN10: 9812771115
• Format: Hardcover
• Copyright: 2008-01-25
• Publisher: World Scientific Pub Co Inc

Summary

"This book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researchers in nonlinear dynamics."--BOOK JACKET.

Table of Contents

Introduction	p. 1
Differential Geometry of Flows	p. 23
Global Transversality in Continuous Dynamical Systems	p. 63
Chaotic Layer Dynamics	p. 113
Two-Dimensional Stochastic Layers	p. 153
Stochasticity in Resonant Separatrix Layers	p. 197
Nonlinear Dynamics on an Equi-energy Surface	p. 253
Stability and Grazing in Dissipative Systems	p. 289
Global Dynamics in Two-dimensional Dynamical Systems	p. 341
Flow Switchability in Discontinuous Dynamical Systems	p. 379
References	p. 437
Subject Index	p. 445
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