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In the past ten years, there has been much progress in
understanding the global dynamics of systems with several
degrees-of-freedom. An important tool in these studies has been the
theory of normally hyperbolic invariant manifolds and foliations of
normally hyperbolic invariant manifolds. In recent years these
techniques have been used for the development of global
perturbation methods, the study of resonance phenomena in coupled
oscillators, geometric singular perturbation theory, and the study
of bursting phenomena in biological oscillators. "Invariant
manifold theorems" have become standard tools for applied
mathematicians, physicists, engineers, and virtually anyone working
on nonlinear problems from a geometric viewpoint. In this book, the
author gives a self-contained development of these ideas as well as
proofs of the main theorems along the lines of the seminal works of
Fenichel. In general, the Fenichel theory is very valuable for many
applications, but it is not easy for people to get into from
existing literature. This book provides an excellent avenue to
that. Wiggins also describes a variety of settings where these
techniques can be used in applications.
In the past ten years, there has been much progress in
understanding the global dynamics of systems with several
degrees-of-freedom. An important tool in these studies has been the
theory of normally hyperbolic invariant manifolds and foliations of
normally hyperbolic invariant manifolds. In recent years these
techniques have been used for the development of global
perturbation methods, the study of resonance phenomena in coupled
oscillators, geometric singular perturbation theory, and the study
of bursting phenomena in biological oscillators. "Invariant
manifold theorems" have become standard tools for applied
mathematicians, physicists, engineers, and virtually anyone working
on nonlinear problems from a geometric viewpoint. In this book, the
author gives a self-contained development of these ideas as well as
proofs of the main theorems along the lines of the seminal works of
Fenichel. In general, the Fenichel theory is very valuable for many
applications, but it is not easy for people to get into from
existing literature. This book provides an excellent avenue to
that. Wiggins also describes a variety of settings where these
techniques can be used in applications.
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