Chaotic Transport in Dynamical Systems / Edition 1

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Overview

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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Editorial Reviews

Booknews
Wiggins (applied mathematics, California Institute of Technology) gives a highly personal account of the mathematical modeling of transport between qualitatively different motions in dynamical systems, which occurs in a range of disciplines from fluid and celestial mechanics to control theory and chemistry. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781441930965
  • Publisher: Springer New York
  • Publication date: 12/7/2010
  • Series: Interdisciplinary Applied Mathematics Series , #2
  • Edition description: Softcover reprint of hardcover 1st ed. 1992
  • Edition number: 1
  • Pages: 301
  • Product dimensions: 0.66 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

1 Introduction and Examples.- 2 Transport in Two-Dimensional Maps: General Principles and Results.- 3 Convective Mixing and Transport Problems in Fluid Mechanics.- 4 Transport in Quasiperiodically Forced Systems: Dynamics Generated by Sequences of Maps.- 5 Markov Models.- 6 Transport in k-Degree-of-Freedom Hamiltonian Systems, 3 ? k < ?: The Generalization of Separatrices to Higher Dimensions and Their Geometrical Structure.- Appendix 1 Proofs of Theorems 2.6 and 2.12.- Appendix 2 Derivation of the Quasiperiodic Melnikov Functions from Chapter 4.- References.
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