Chaotic Transport in Dynamical Systems

Stephen Wiggins (auth.)9780387975221, 0-387-97522-5, 3-540-97522-5

Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems from the viewpoint of problems of phase space transport are raised in this monograph. Illustrating phase space transport problems arising in a variety of applications that can be modeled as time-periodic perturbations of planar Hamiltonian systems, the book begins with the study of transport in the associated two-dimensional Poincaré Map. This serves as a starting point for the further motivation of the transport issues through the development of ideas in a non-perturbative framework with generalizations to higher dimensions as well as more general time dependence. A timely and important contribution to those concerned with the applications of mathematics.

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Table of contents :
Front Matter….Pages i-xiii
Introduction and Examples….Pages 1-15
Transport in Two-Dimensional Maps: General Principles and Results….Pages 17-79
Convective Mixing and Transport Problems in Fluid Mechanics….Pages 81-120
Transport in Quasiperiodically Forced Systems: Dynamics Generated by Sequences of Maps….Pages 121-191
Markov Models….Pages 193-208
Transport in к -Degree-of-Freedom Hamiltonian Systems, 3 ≤ к < ∞: The Generalization of Separatrices to Higher Dimensions and Their Geometrical Structure….Pages 209-271
Back Matter….Pages 273-301