Topological entropy and partially hyperbolic diffeomorphisms

被引：27

作者：

Hua, Yongxia ^{[1
]}

Saghin, Radu ^{[2
]}

Xia, Zhihong ^{[1
]}

机构：

[1] NW Univ, Dept Math, Evanston, IL 60208 USA

[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2008年 / 28卷

关键词：

D O I：

10.1017/S0143385707000405

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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(infinity) 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.

引用

页码：843 / 862

页数：20