Strictly Ergodic Models Under Face and Parallelepiped Group Actions  

作　　者：Wen Huang Song Shao Xiangdong Ye 

机构地区：[1]Wu Wen-Tsun Key Laboratory of Mathematics,USTC,Chinese Academy of Sciences,Hefei 230026,Anhui,People's Republic of China [2]Department of Mathematics,University of Science and Technology of China,Hefei 230026,Anhui,People's Republic of China

出　　处：《Communications in Mathematics and Statistics》2017年第1期93-122,共30页数学与统计通讯（英文）

基　　金：NNSF for Distinguished Young Schooler(11225105);all authors aresupported by NNSF of China(11371339,11431012,11571335)and by the Fundamental Research Fundsfor the Central Universities.

摘　　要：The Jewett-Krieger theorem states that each ergodic system has a strictlyergodic topological model.In this article,we show that for an ergodic system onemay require more properties on its strictly ergodic model.For example,the orbitclosure of points in diagonal under face transforms may be also strictly ergodic.Asan application,we show the pointwise convergence of ergodic averages along cubes,which was firstly proved by Assani(J Anal Math 110:241-269,2010).

关 键 词：Ergodic averages Model CUBES Face transformations 

分 类 号：O17[理学—数学]