A C1 closing lemma for nonuniformly partially hyperbolic diffeomorphisms of class C1+α

被引：1

作者：

Hayashi, Shuhei ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Tokyo, Japan

来源：

DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL | 2015年 / 30卷 / 04期

关键词：

a closing lemma; nonhyperbolic ergodic measures; dominated splittings; strong stable and unstable manifolds;

D O I：

10.1080/14689367.2015.1055320

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a C-1 closing lemma for C1+ diffeomorphisms under the existence of dominated splittings associated with the Lyapunov splittings over the supports of ergodic measures, which creates a sequence of periodic orbits having the local strong stable and unstable manifolds with uniform sizes over some compact set whose measure arbitrarily close to 1. This corresponds to Pesin's stable and unstable manifolds theorem for nonuniformly hyperbolic diffeomorphisms of class C1+alpha.

引用

页码：355 / 368

页数：14