Normally hyperbolic invariant manifolds : the noncompact case
- Eldering, Jaap, author.
- [Paris] : Atlantis Press, 
- Copyright notice
- Physical description
- xii, 189 pages : illustrations ; 25 cm.
QA685 .E43 2013
- Unknown QA685 .E43 2013
- Includes bibliographical references (pages 183-186) and index.
- Introduction.- Manifolds of bounded geometry.- Persistence of noncompact NHIMs.- Extension of results.
- (source: Nielsen Book Data)
- 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)
- Publication date
- Copyright date
- Jaap Eldering.
- Atlantis series in dynamical systems ; volume 2