Normally hyperbolic invariant manifolds : the noncompact case
- Responsibility
- Jaap Eldering.
- Language
- English.
- Publication
- [Paris] : Atlantis Press, [2013]
- Copyright notice
- ©2013
- Physical description
- xii, 189 pages : illustrations ; 25 cm.
- Series
- Atlantis series in dynamical systems ; volume 2
Access
Math & Statistics Library
Stacks
| Call number | Status |
|---|---|
| QA685 .E43 2013 |
More options
Creators/Contributors
- Author/Creator
- Eldering, Jaap, author.
Contents/Summary
- Bibliography
- Includes bibliographical references (pages 183-186) and index.
- Contents
-
- Introduction.- Manifolds of bounded geometry.- Persistence of noncompact NHIMs.- Extension of results.
- (source: Nielsen Book Data)9789462390027 20160612
- Publisher's 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.
(source: Nielsen Book Data)9789462390027 20160612
Subjects
Bibliographic information
- Publication date
- 2013
- Copyright date
- 2013
- ISBN
- 9789462390027 (hbk.)
- 9462390029 (hbk.)
- 9789462390034 (ebk.)
- 9462390037 (ebk.)
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