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" Normally hyperbolic invariant manifolds "
Jaap Eldering
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BL
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| Record Number
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594993
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b424212
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| Main Entry
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Eldering, Jaap
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| Title & Author
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Normally hyperbolic invariant manifolds : the noncompact case /\ Jaap Eldering
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| Publication Statement
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New York :: Atlantis Press,, c2013
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| Series Statement
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Atlantis series in dynamical systems,; v. 2
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| Page. NO
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1 online resource (xii, 189 pages) :: illustrations
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| ISBN
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9462390037 (electronic bk.)
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: 9789462390034 (electronic bk.)
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9789462390027
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9789462390034
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| Bibliographies/Indexes
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Includes bibliographical references and index
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| Contents
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Introduction -- Manifolds of bounded geometry -- Persistence of noncompact NHIMs -- Extension of results
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| Abstract
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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
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| Subject
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Geometry, Differential
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| Subject
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Hyperbolic spaces
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Invariant manifolds
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| Dewey Classification
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515/.352
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| LC Classification
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QA614.8.E54 2013eb
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QA614.8.E54 2013eb
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| Added Entry
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Ohio Library and Information Network
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