Topological entropy and partially hyperbolic diffeomorphisms

Yongxia Hua, RADU SAGHIN , Zhihong Xia

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We consider partially hyperbolic diffeomorphisms on compact manifolds. We define the notion of the unstable and stable foliations stably carrying some unique non-trivial homologies. Under this topological assumption, 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 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.

Original languageEnglish
Pages (from-to)843-862
Number of pages20
JournalErgodic Theory and Dynamical Systems
Volume28
Issue number3
DOIs
StatePublished - 1 Jun 2008

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