TY  - BOOK
AU  - Eldering,Jaap
ED  - SpringerLink (Online service)
TI  - Normally Hyperbolic Invariant Manifolds: The Noncompact Case 
T2  - Atlantis Series in Dynamical Systems
SN  - 9789462390034
AV  - QA313 
U1  - 515.39 23
PY  - 2013///
CY  - Paris
PB  - Atlantis Press, Imprint: Atlantis Press
KW  - Mathematics
KW  - Dynamics
KW  - Ergodic theory
KW  - Dynamical Systems and Ergodic Theory
KW  - Mathematics, general
N1  - Introduction -- Manifolds of bounded geometry -- Persistence of noncompact NHIMs -- Extension of results
N2  - 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
UR  - http://dx.doi.org/10.2991/978-94-6239-003-4
ER  -