Topological Entropy and Partially Hyperbolic Diffeomorphisms

Details Topological Entropy and Partially Hyperbolic Diffeomorphisms Topological Entropy and Partially Hyperbolic Diffeomorphisms

2006-08-29

arxiv.org/abs/math/0608720v1

Mathematics

Dynamical Systems

Scientific paper

We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique non-trivial homologies. We prove the following two results: if the center foliation is one dimensional, then the topological entropy is locally a constant; and if the center foliation is two dimensional, then the topological entropy is continuous on the set of all $C^\8$ diffeomorphisms. The proof uses a topological invariant we introduced; Yomdin's theorem on upper semi-continuity; Katok's theorem on lower semi-continuity for two dimensional systems and a refined Pesin-Ruelle inequality we proved for partially hyperbolic diffeomorphisms.

Affiliated with

Also associated with

No associations

Rating

Topological Entropy and Partially Hyperbolic Diffeomorphisms 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 Topological Entropy and Partially Hyperbolic Diffeomorphisms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological Entropy and Partially Hyperbolic Diffeomorphisms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-334060