Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry

Details Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry

2012-04-05

arxiv.org/abs/1204.1310v1

Mathematics

Dynamical Systems

PhD thesis, 151 pages, 14 figures, preliminary version

Scientific paper

We prove a persistence result for noncompact normally hyperbolic invariant manifolds in the setting of Riemannian manifolds of bounded geometry. Bounded geometry of the ambient manifold is a crucial assumption required to control the uniformity of all estimates throughout the proof. The $C^{k,\alpha}$-smoothness result is optimal with respect to the spectral gap condition involved. The core of the persistence proof is based on the Perron method. In the process we derive new results on noncompact submanifolds in bounded geometry: a uniform tubular neighborhood theorem and uniform smooth approximation of a submanifold. The submanifolds considered are assumed to be uniformly $C^k$ bounded in an appropriate sense.

Affiliated with

Also associated with

No associations

Rating

Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-213411