Ebook: Chaotic Transport in Dynamical Systems

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.

---

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 Poincar? 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.

---

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 Poincar? 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.
Content:
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

---

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 Poincar? 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.
Content:
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
....