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.
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)
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.