SHADOWING, EXPANSIVENESS AND SPECIFICATION FOR C1-CONSERVATIVE SYSTEMS

被引：17

作者：

Bessa, Mario ^{[1
]}

Lee, Manseob ^{[2
]}

Wen, Xiao ^{[3
]}

机构：

[1] Univ Beira Interior, P-6201001 Covilha, Portugal

[2] Mokwon Univ, Dept Math, Taejon 302729, South Korea

[3] Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2015年 / 35卷 / 03期

基金：

新加坡国家研究基金会; 中国国家自然科学基金;

关键词：

Shadowing; expansiveness; specification; generic; Anosov; volume-preserving; star systems; SYMBOLIC EXTENSIONS; PERIODIC POINTS; DIFFEOMORPHISMS; HYPERBOLICITY; STABILITY; ABUNDANCE; PROPERTY; FLOWS;

D O I：

10.1016/S0252-9602(15)30005-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a C-1-generic volume-preserving dynamical system (diffeomorphism or flow) has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, as in [10, 27], we prove that the C-1-robustness, within the volume-preserving context, of the expansiveness property and the weak specification property, imply that the dynamical system (diffeomorphism or flow) is Anosov.

引用

页码：583 / 600

页数：18

共 50 条

[1]

Abdenur F, 2007, DISCRETE CONT DYN-A, V17, P223

[2] Homoclinic classes with shadowing [J].