Multidimensional Local Central Limit Theorem of Some Non-uniformly Hyperbolic Systems  

作　　者：Hong Qiang XIA 

机构地区：[1]College of Science, Wuhan University of Science and Engineering, No. 1 Fangzhi Road, Wuhan 430073, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第4期565-580,共16页数学学报（英文版）

摘　　要：We consider Young＇s nonuniformly hyperbolic system （X, T, u） where u is the SRB measure corresponding to the system （X, T）, and show that if the components of a Holder observable f ： X → R^d are cohomologously independent, then f satisfies the multidimensional central limit theorem. Moreover if f is aperiodic, then f satisfies the local multidimensional central limit theorem.We consider Young＇s nonuniformly hyperbolic system （X, T, u） where u is the SRB measure corresponding to the system （X, T）, and show that if the components of a Holder observable f ： X → R^d are cohomologously independent, then f satisfies the multidimensional central limit theorem. Moreover if f is aperiodic, then f satisfies the local multidimensional central limit theorem.

关 键 词：central limit theorem transfer operator nonuniform hyperbolic diIQ[eomorphism 

分 类 号：O211.4[理学—概率论与数理统计] O175.27[理学—数学]