ROBUST WEAK ERGODICITY AND STABLE ERGODICITY

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

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

ROBUST WEAK ERGODICITY AND STABLE ERGODICITY

周云华

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

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/Abstract

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.

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

Abstract:

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

中图分类号:

37D30

周云华. ROBUST WEAK ERGODICITY AND STABLE ERGODICITY[J]. 数学物理学报(英文版), 2013, 33(5): 1375-1381.

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

参考文献

[1] Abdenur F, Avila A, Bochi J. Robust transitivity and topological mixing for C1-flows. Proc Amer Math Soc, 2004, 132(3): 699–705

[2] Arbieto A, Matheus C, Pacifico M. The bernoulli property for weakly hyperbolic systems. J Stat Phys, 2004, 117: 243–260

[3] Avila A. On the regularization of conservative maps. Acta Math, 2010, 205: 5–18

[4] Burns K, Dolgopyat D, Pesin Ya. Partial hyperbolicity, Lyapunov exponents and stable ergodicity. J Stat Phys, 2002, 108: 927–942

[5] Bonatti C, D´?az L, Viana M. Dynamics Beyond Uniform Hyperbolicity. Springer, 2005

[6] Bonatti C, Matheus C, Viana M, Wilkinson A. Abundance of stable ergodicity. Comment Math Helv, 2004, 79: 753–757

[7] Bonatti C, Viana M. SRB measures for partially hyperbolic systems whose central direction is mostly contracting. Israel J Math, 2000, 115: 157–193

[8] D´?az L, Pujals E, Ures R. Partial hyperbolicity and robust transitivity. Acta Math, 1999, 183: 1–43

[9] Dolgopyat D, Wilkinson A. Stable acessibility is C1 dense. Ast´erisque, 2003, 287: 33–60

[10] Furstenberg H. Strict ergodicity and transformations of the torus. Amer J Math, 1961, 83: 573–601

[11] Rodr´?guez Hertz F, Rodr´?guez Hertz M A. Ures R. Accessibility and stable ergodicity for partially hyperbolic
diffeomorphisms with 1D-center bundle. Invent Math, 2008, 172: 353–381

[12] Pesin Ya. Lectures on Partial Hyperbolicity and Stable Ergodicity. Z¨urich Lectures in Advanced Mathematics.
European Mathematical Society, 2004

[13] Pugh C, Shub M. Stably ergodic dynamical systems and partial hyperbolicity. J Complexty, 1997, 13: 125–179

[14] Tahzibi A. Robust transitivity and almost robust ergodicity. Erg Th Dyn Sys, 2004, 24: 1261–1269

[15] Tahzibi A. Stably ergodic diffeomorphisms which are not partially hyperbolic. Israel J Math, 2004 142: 315–344

ROBUST WEAK ERGODICITY AND STABLE ERGODICITY

ROBUST WEAK ERGODICITY AND STABLE ERGODICITY

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