ROBUST WEAK ERGODICITY AND STABLE ERGODICITY  

作　　者：周云华 

机构地区：[1]College of Mathematics and Statistics, Chongqing University

出　　处：《Acta Mathematica Scientia》2013年第5期1375-1381,共7页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(11001284);Natural Science Foundation Project of CQ CSTC(cstcjjA00003);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 C^r（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 C^r（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.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 C^r（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 C^r（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 ergodieity almost robust ergodicity Lyapunov exponent 

分 类 号：O177.99[理学—数学]