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Normally Hyperbolic Invariant Manifolds: The Noncompact Case Softcover Repri Edition
Contributor(s): Eldering, Jaap (Author)
ISBN: 9462390428     ISBN-13: 9789462390423
Publisher: Atlantis Press
OUR PRICE:   $52.24  
Product Type: Paperback - Other Formats
Published: October 2015
Qty:
Temporarily out of stock - Will ship within 2 to 5 weeks
Additional Information
BISAC Categories:
- Mathematics | Mathematical Analysis
- Science | System Theory
Dewey: 510
Series: Atlantis Studies in Dynamical Systems
Physical Information: 0.43" H x 6.14" W x 9.21" (0.64 lbs) 189 pages
 
Descriptions, Reviews, Etc.
Publisher 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.