Normally Hyperbolic Invariant Manifolds: The Noncompact Case - Atlantis Studies in Dynamical Systems 2 (Hardback)
  • Normally Hyperbolic Invariant Manifolds: The Noncompact Case - Atlantis Studies in Dynamical Systems 2 (Hardback)
zoom

Normally Hyperbolic Invariant Manifolds: The Noncompact Case - Atlantis Studies in Dynamical Systems 2 (Hardback)

(author)
£74.99
Hardback 189 Pages / Published: 26/08/2013
  • We can order this

Usually dispatched within 3 weeks

  • This item has been added to your basket

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.

Publisher: Atlantis Press (Zeger Karssen)
ISBN: 9789462390027
Number of pages: 189
Weight: 4321 g
Dimensions: 235 x 155 x 12 mm
Edition: 2013 ed.

You may also be interested in...

Reviews

Please sign in to write a review

Your review has been submitted successfully.