Normally hyperbolic invariant manifolds in dynamical systems
by Stephen Wiggins
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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Subjects
Invariant manifolds, Differentiable dynamical systems, Hyperbolic spaces, Invariants, Geometry, non-euclidean, Hyperspace, Manifolds (mathematics), Mechanics, Manifolds and Cell Complexes (incl. Diff.Topology), Mathematics, Cell aggregation, Dynamical Systems and Complexity Statistical Physics| Edition | Availability |
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1
Normally Hyperbolic Invariant Manifolds in Dynamical Systems
Dec 01, 2013, Springer
paperback
1461243130 9781461243137
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2
Normally Hyperbolic Invariant Manifolds in Dynamical Systems
Nov 26, 2013, Springer
paperback
1461287340 9781461287346
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3
Normally Hyperbolic Invariant Manifolds in Dynamical Systems
2013, Springer London, Limited
in English
1461243122 9781461243120
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4
Normally hyperbolic invariant manifolds in dynamical systems
1994, Springer-Verlag
in English
038794205X 9780387942056
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Book Details
Edition Notes
Includes bibliographical references (p. [185]-190) and index.
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- Created April 1, 2008
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