数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (5): 1375-1381.doi: 10.1016/S0252-9602(13)60088-0

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ROBUST WEAK ERGODICITY AND STABLE ERGODICITY

周云华   

  1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
  • 收稿日期:2011-10-08 修回日期:2012-08-27 出版日期:2013-09-20 发布日期:2013-09-20
  • 基金资助:

    This work has been supported by National Natural Science Foundation of China (11001284), Natural Science Foundation Project of CQ CSTC(cstcjjA00003) and Fundamental Research Funds for the Central Universities (CQDXWL2012008).

ROBUST WEAK ERGODICITY AND STABLE ERGODICITY

 ZHOU Yun-Hua   

  1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
  • Received:2011-10-08 Revised:2012-08-27 Online:2013-09-20 Published:2013-09-20
  • Supported by:

    This work has been supported by National Natural Science Foundation of China (11001284), Natural Science Foundation Project of CQ CSTC(cstcjjA00003) and Fundamental Research Funds for the Central Universities (CQDXWL2012008).

摘要:

In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a Cr(r > 1) conservative partially hyperbolic diffeomorphism is stably ergodic if it is robustly weakly ergodic and has positive (or negative) central exponents
on a positive measure set. Furthermore, if the condition of robust weak ergodicity is replaced by weak ergodicity, then the diffeomophism is an almost stably ergodic system. Additionally, we show in dimension three, a Cr(r > 1) conservative partially hyperbolic diffeomorphism can be approximated by stably ergodic systems if it is robustly weakly ergodic and robustly has non-zero central exponents.

关键词: weak ergodicity, stable ergodicity, almost robust ergodicity, Lyapunov ex-ponent

Abstract:

In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a Cr(r > 1) conservative partially hyperbolic diffeomorphism is stably ergodic if it is robustly weakly ergodic and has positive (or negative) central exponents
on a positive measure set. Furthermore, if the condition of robust weak ergodicity is replaced by weak ergodicity, then the diffeomophism is an almost stably ergodic system. Additionally, we show in dimension three, a Cr(r > 1) conservative partially hyperbolic diffeomorphism can be approximated by stably ergodic systems if it is robustly weakly ergodic and robustly has non-zero central exponents.

Key words: weak ergodicity, stable ergodicity, almost robust ergodicity, Lyapunov ex-ponent

中图分类号: 

  • 37D30