ROBUST WEAK ERGODICITY AND STABLE ERGODICITY

doi:10.1016/S0252-9602(13)60088-0

Acta mathematica scientia,Series B ›› 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

ZHOU Yun-Hua

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).

Abstract

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 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.

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

CLC Number:

37D30

ZHOU Yun-Hua. ROBUST WEAK ERGODICITY AND STABLE ERGODICITY[J].Acta mathematica scientia,Series B, 2013, 33(5): 1375-1381.

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ROBUST WEAK ERGODICITY AND STABLE ERGODICITY

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