Unique Ergodicity for Zero-entropy Dynamical Systems with the Approximate Product Property  

作　　者：Peng SUN 

机构地区：[1]China Economics and Management Academy,Central University of Finance and Economics,Beijing 100081,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第2期362-376,共15页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11571387);CUFE Young Elite Teacher Project(Grant No.QYP1902)。

摘　　要：We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover, we show that unique ergodicity implies the approximate product property if the system has periodic points.

关 键 词：Approximate product property unique ergodicity topological entropy ergodic measure MINIMALITY specification gluing orbit interval map periodic points 

分 类 号：O19[理学—数学]