A geometrical proof of the persistence of normally hyperbolic submanifolds

Details A geometrical proof of the persistence of normally hyperbolic submanifolds A geometrical proof of the persistence of normally hyperbolic submanifolds

2011-09-15

arxiv.org/abs/1109.3280v1

Mathematics

Dynamical Systems

Scientific paper

We present a simple, computation free and geometrical proof of the following classical result: for a diffeomorphism of a manifold, any compact submanifold which is invariant and normally hyperbolic persists under small perturbations of the diffeomorphism. The persistence of a Lipschitz invariant submanifold follows from an application of the Schauder fixed point theorem to a graph transform, while smoothness and uniqueness of the invariant submanifold are obtained through geometrical arguments. Moreover, our proof provides a new result on persistence and regularity of "topologically" normally hyperbolic submanifolds, but without any uniqueness statement.

Affiliated with

Also associated with

No associations

Rating

A geometrical proof of the persistence of normally hyperbolic submanifolds 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 A geometrical proof of the persistence of normally hyperbolic submanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A geometrical proof of the persistence of normally hyperbolic submanifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-673103