Hyperbolicity of C 1-star invariant sets for C 1-class dynamical systems

被引：3

作者：

Dai XiongPing ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2011年 / 54卷 / 02期

基金：

中国国家自然科学基金;

关键词：

autonomous differential system; star property; hyperbolicity; EXPANSIVE HOMOCLINIC CLASSES; SHADOWABLE CHAIN COMPONENTS; SATISFY AXIOM; CLOSING LEMMA;

D O I：

10.1007/s11425-010-4090-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we simply prove, in the framework of Liao, the hyperbolicity of C (1)-star invariant sets of C (1)-class differential systems on a closed manifold of dimension a (c) 1/2 4, without using the C (1)-connecting lemma and even the ergodic closing lemma.

引用

页码：269 / 280

页数：12

共 8 条

[1] Hyperbolicity of C1-star invariant sets for C1-class dynamical systems
XiongPing Dai
Science China Mathematics, 2011, 54 : 269 - 280
[2] Hyperbolicity of C1 -star invariant sets for C1 -class dynamical systems
DAI XiongPing Department of Mathematics
ScienceChina(Mathematics), 2011, 54 (02) : 269 - 280
[3] HYPERBOLICITY OF C1-STABLY EXPANSIVE HOMOCLINIC CLASSES
Lee, Keonhee
Lee, Manseob
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 27 (03) : 1133 - 1145
[4] HYPERBOLICITY AND TYPES OF SHADOWING FOR C1 GENERIC VECTOR FIELDS
Ribeiro, Raquel
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (07) : 2963 - 2982
[5] Rigidity for C1 actions on the interval arising from hyperbolicity I: solvable groups
Bonatti, C.
Monteverde, I.
Navas, A.
Rivas, C.
MATHEMATISCHE ZEITSCHRIFT, 2017, 286 (3-4) : 919 - 949
[6] C1-persistently continuum-wise expansive homoclinic classes and recurrent sets
Das, Tarun
Lee, Keonhee
Lee, Manseob
TOPOLOGY AND ITS APPLICATIONS, 2013, 160 (02) : 350 - 359
[7] SHADOWING, EXPANSIVENESS AND SPECIFICATION FOR C1-CONSERVATIVE SYSTEMS
Bessa, Mario
Lee, Manseob
Wen, Xiao
ACTA MATHEMATICA SCIENTIA, 2015, 35 (03) : 583 - 600
[8] Rigidity for C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document} actions on the interval arising from hyperbolicity I: solvable groups
C. Bonatti
I. Monteverde
A. Navas
C. Rivas
Mathematische Zeitschrift, 2017, 286 (3-4) : 919 - 949

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