Topological Entropy and Partially Hyperbolic Diffeomorphisms

• DOI: 10.48550/arxiv.math/0608720
• Publication Date: 2006-01-01
• Authors: Yongxia Hua; Radu Saghin; Zhihong Xia
• Keywords: Topological Entropy; Foliation (geology)

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