数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (2): 552-558.doi: 10.1016/S0252-9602(12)60037-X

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DIFFEOMORPHISMS WITH VARIOUS C1 STABLE PROPERTIES

田学廷|孙文祥   

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China|Departamento de Matem´atica, Universidade Federal de Alagoas, Macei´o 57072-090, Brazil LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
  • 收稿日期:2009-08-05 修回日期:2011-02-27 出版日期:2012-03-20 发布日期:2012-03-20
  • 基金资助:

    Tian is the corresponding author and supported by CAPES(Brazil); Sun is supported by National Natural Science Foundation (10671006, 10831003) and National Basic Research Program of China (973 Program) (2006CB805903).

DIFFEOMORPHISMS WITH VARIOUS C1 STABLE PROPERTIES

 TIAN Xue-Ting, SUN Wen-Xiang   

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China|Departamento de Matem´atica, Universidade Federal de Alagoas, Macei´o 57072-090, Brazil LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Received:2009-08-05 Revised:2011-02-27 Online:2012-03-20 Published:2012-03-20
  • Supported by:

    Tian is the corresponding author and supported by CAPES(Brazil); Sun is supported by National Natural Science Foundation (10671006, 10831003) and National Basic Research Program of China (973 Program) (2006CB805903).

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摘要：

Let M be a smooth compact manifold and ∧ be a compact invariant set. In this article, we prove that, for every robustly transitive set ∧, f|∧ satisfies a C1-generic-stable shadowable property (resp., C1-generic-stable transitive specification property or C1-generic-stable barycenter property) if and only if ∧ is a hyperbolic basic set. In partic-ular, f|∧ satisfies a C1-stable shadowable property (resp., C1-stable transitive specification property or C1-stable barycenter property) if and only if ∧ is a hyperbolic basic set. Similar results are valid for volume-preserving case.

关键词: Specification property, hyperbolic basic set, topologically transitive, shad-owing property

Abstract:

Let M be a smooth compact manifold and ∧ be a compact invariant set. In this article, we prove that, for every robustly transitive set ∧, f|∧ satisfies a C1-generic-stable shadowable property (resp., C1-generic-stable transitive specification property or C1-generic-stable barycenter property) if and only if ∧ is a hyperbolic basic set. In partic-ular, f|∧ satisfies a C1-stable shadowable property (resp., C1-stable transitive specification property or C1-stable barycenter property) if and only if ∧ is a hyperbolic basic set. Similar results are valid for volume-preserving case.

Key words: Specification property, hyperbolic basic set, topologically transitive, shad-owing property

中图分类号: 

  • 37A25
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