HYPERBOLIC PERIODIC POINTS FOR CHAIN HYPERBOLIC HOMOCLINIC CLASSES

被引：8
|
作者：
Sun, Wenxiang [1 ]
Yang, Yun [1 ]
机构：
[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 07期
关键词：
Chain hyperbolicity; closing property; growth of periodic points; topological entropy; maximal entropy measures; AXIOM-A-DIFFEOMORPHISMS;
D O I：
10.3934/dcds.2016.36.3911
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we establish a closing property and a hyperbolic closing property for thin trapped chain hyperbolic homoclinic classes with one dimensional center in partial hyperbolicity setting. Taking advantage of theses properties, we prove that the growth rate of the number of hyperbolic periodic points is equal to the topological entropy. We also obtain that the hyperbolic periodic measures are dense in the space of invariant measures.
引用
收藏
页码：3911 / 3925
页数：15
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