Normally hyperbolic invariant manifolds : the noncompact case /

Normally hyperbolic invariant manifolds : the noncompact case /

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Bibliographic Details
Author / Creator:	Eldering, Jaap.
Imprint:	New York : Springer, 2013.
Description:	1 online resource (xii, 189 pages) : illustrations.
Language:	English
Series:	Atlantis series in dynamical systems, 2213-3526 ; v. 2 Atlantis series in dynamical systems ; v. 2.
Subject:	Hyperbolic spaces. Invariant manifolds. Geometry, Differential. Geometry, Differential. Hyperbolic spaces. Invariant manifolds.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/9852574

Hidden Bibliographic Details
ISBN:	9789462390034 (electronic bk.) 9462390037 (electronic bk.) 9789462390027 9789462390034
Notes:	Includes bibliographical references and index.
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.
Standard no.:	10.2991/978-94-6239-003-4

Description
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.
Physical Description:	1 online resource (xii, 189 pages) : illustrations.
Bibliography:	Includes bibliographical references and index.
ISBN:	9789462390034 9462390037 9789462390027 9789462390034
ISSN:	2213-3526 ;