Normally hyperbolic invariant manifolds the noncompact case Jaap Eldering

Format:

Book

Author/Creator:

Eldering, Jaap

Series:

Atlantis series in dynamical systems v. 2

Atlantis series in dynamical systems 2213-3526 v. 2

Language:

English

Subjects (All):

Hyperbolic spaces.

Invariant manifolds.

Geometry, Differential.

Physical Description:

1 online resource

Place of Publication:

New York Springer 2013

Summary:

This monograph treats normally hyperbolic invariant manifolds, with a focus on noncompactness. These objects generalize hyperbolic fixed points and are ubiquitous in dynamical systems. First, normally hyperbolic invariant manifolds and their relation to hyperbolic fixed points and center manifolds, as well as, overviews of history and methods of proofs are presented. Furthermore, issues (such as uniformity and bounded geometry) arising due to noncompactness are discussed in great detail with examples. The main new result shown is a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. This extends well-known results by Fenichel and Hirsch, Pugh and Shub, and is complementary to noncompactness results in Banach spaces by Bates, Lu and Zeng. Along the way, some new results in bounded geometry are obtained and a framework is developed to analyze ODEs in a differential geometric context. Finally, the main result is extended to time and parameter dependent systems and overflowing invariant manifolds

Contents:

Introduction Manifolds of bounded geometry Persistence of noncompact NHIMs Extension of results

Notes:

Includes bibliographical references and index

ISBN:

9789462390034

9462390037

OCLC:

859159018

Access Restriction:

Restricted for use by site license