数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (3): 583-600.doi: 10.1016/S0252-9602(15)30005-9

• 论文 • 上一篇    下一篇

SHADOWING, EXPANSIVENESS AND SPECIFICATION FOR C1-CONSERVATIVE SYSTEMS

Mário BESSA1, Manseob LEE2, 文晓3   

  1. 1. Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã, Portugal;
    2. Department of Mathematics, Mokwon University, Daejeon 302-729, Korea;
    3. The School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
  • 收稿日期:2014-01-13 修回日期:2014-06-15 出版日期:2015-05-01 发布日期:2015-05-01
  • 基金资助:

    MB was partially supported by National Funds through FCT - “Fundação para a Ciência e a Tecnologia”, (PEst-OE/MAT/UI0212/2011); ML was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry, ICT & Future Planning (No.2014R1A1A1A05002124); XW was supported by National Natural Science Foundation of China (No.11301018 and 11371046).

SHADOWING, EXPANSIVENESS AND SPECIFICATION FOR C1-CONSERVATIVE SYSTEMS

Mário BESSA1, Manseob LEE2, Xiao WEN3   

  1. 1. Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã, Portugal;
    2. Department of Mathematics, Mokwon University, Daejeon 302-729, Korea;
    3. The School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
  • Received:2014-01-13 Revised:2014-06-15 Online:2015-05-01 Published:2015-05-01
  • Supported by:

    MB was partially supported by National Funds through FCT - “Fundação para a Ciência e a Tecnologia”, (PEst-OE/MAT/UI0212/2011); ML was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry, ICT & Future Planning (No.2014R1A1A1A05002124); XW was supported by National Natural Science Foundation of China (No.11301018 and 11371046).

摘要:

We prove that a C1-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 C1-robustness, within the volume-preserving context, of the expansiveness property and the weak specifica- tion property, imply that the dynamical system (diffeomorphism or flow) is Anosov.

关键词: Shadowing, expansiveness, specification, generic, Anosov, volume-preserving, star systems

Abstract:

We prove that a C1-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 C1-robustness, within the volume-preserving context, of the expansiveness property and the weak specifica- tion property, imply that the dynamical system (diffeomorphism or flow) is Anosov.

Key words: Shadowing, expansiveness, specification, generic, Anosov, volume-preserving, star systems

中图分类号: 

  • 37C20