Normally Hyperbolic Invariant Manifolds is popular PDF and ePub book, written by Jaap Eldering in 2013-08-17, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Normally Hyperbolic Invariant Manifolds can be Read Online from any device for your convenience.
Normally Hyperbolic Invariant Manifolds Book PDF 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.
Detail Book of Normally Hyperbolic Invariant Manifolds PDF
- Author : Jaap Eldering
- Release : 17 August 2013
- Publisher : Springer Science & Business Media
- ISBN : 9789462390034
- Genre : Mathematics
- Total Page : 197 pages
- Language : English
- PDF File Size : 19,5 Mb
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