Normally Hyperbolic Invariant Manifolds
The Noncompact Case
(Sprache: Englisch)
This book covers normally hyperbolic invariant manifolds and their relation to hyperbolic fixed points and center manifolds, and offers a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry.
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This book covers normally hyperbolic invariant manifolds and their relation to hyperbolic fixed points and center manifolds, and offers a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry.
Klappentext zu „Normally Hyperbolic Invariant Manifolds “
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.
Inhaltsverzeichnis zu „Normally Hyperbolic Invariant Manifolds “
Introduction.- Manifolds of bounded geometry.- Persistence of noncompact NHIMs.- Extension of results.
Bibliographische Angaben
- Autor: Jaap Eldering
- 2013, XII, 189 Seiten, Masse: 16,1 x 23,9 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 9462390029
- ISBN-13: 9789462390027
Sprache:
Englisch
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