Téléchargez le livre : Normally Hyperbolic Invariant Manifolds

Normally Hyperbolic Invariant Manifolds

The Noncompact Case

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Éditeur :

Atlantis Press


Paru le : 2013-08-17



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Description

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.
Pages
189 pages
Collection
n.c
Parution
2013-08-17
Marque
Atlantis Press
EAN papier
9789462390027
EAN EPUB
9789462390034
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
18
Taille du fichier
4301 Ko
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Prix
52,74 €

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