Topological Entropy and Partially Hyperbolic Diffeomorphisms
Dynamical Systems
2011-02-19 v1 Mathematical Physics
math.MP
Abstract
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 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.
Cite
@article{arxiv.math/0608720,
title = {Topological Entropy and Partially Hyperbolic Diffeomorphisms},
author = {Yongxia Hua and Radu Saghin and Zhihong Xia},
journal= {arXiv preprint arXiv:math/0608720},
year = {2011}
}