Bøger af Stephen Wiggins

Presents a series of lectures delivered by Stephen Wiggins at the Fields Institute in early 1993, that is concerned with the geometrical viewpoint of the global dynamics of nonlinear dynamical systems. This work is suitable for engineers and mathematicians who work on issues related to the global dynamics of nonlinear dynamical systems.

Written by a specialist in geophysical fluid dynamics and an applied mathematician, this book provides an accessible introduction to new methods for analysing Lagrangian motion in geophysical flows, and surveys research in geophysical fluid dynamics that makes use of them.

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 Poincare Map.

An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds.

In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds.

This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior.