Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (3): 701-712.doi: 10.1016/S0252-9602(10)60071-9

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LOCAL CENTRAL LIMIT THEOREM AND BERRY-ESSEEN THEOREM FOR SOME NONUNIFORMLY HYPERBOLIC DIFFEOMORPHISMS

XIA Hong-Qiang   

  1. College of Sciene, Wuhan Textile University, No.1 Fangzhi Road, Wuhan 430073, China
  • Received:2006-12-29 Revised:2008-09-30 Online:2010-05-20 Published:2010-05-20
  • Supported by:

    Supported by NSF of China (10571174) and the Scientific Research Foundation of Ministry of Education for Returned Overseas Chinese Scholars, and the Scientific Research Foundation of Ministry of Human and Resources and Social Security of China for Returned Overseas Scholars

Abstract:

We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit
theorem holds, and the speed in the central limit theorem is O(1√n}).

Key words: Local central limit theorem, Berry-Esseen theorem, nonuniform hyperbolic diffeomorphism, Hénon map

CLC Number: 

  • 37C27
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