关于连续变换的遍历性质的一些注记  

Some Notes on Ergodic Properties for Continuous Transformations

作　　者：郭新伟[1] 鲍晓云[2] 

机构地区：[1]山东大学威海分校数学与统计学院,威海264209 [2]九江学院理学院,九江332005

出　　处：《应用泛函分析学报》2010年第4期370-375,共6页Acta Analysis Functionalis Applicata

摘　　要：设(X,d)是一个紧的距离空间,T是(X,d)上的连续变换.利用平均遍历定理证明了:对任意的x∈X,1/n sum from i=0 to n-1 f(T^i x)在C(X)上收敛.该结果是连续变换的Birkhoff型个别遍历定理的推广.由此结果研究了T的其它遍历性质,特别,不依赖深刻的Choquet积分表示定理,给出了遍历分解定理的一个较为简单而直接的证明.Let （X, d） be an compact metric space, T an continuous transformation on （X, d）. It is proved that n/1 n-1∑i=0 f（Tix） converge for any x∈ X using mean ergodic theorem. This result is a strengthening of Birkhoff individual ergodic theorem for continuous transformations. In addition, other ergodic properties of T is also discussed; especially a simple and direct proof of ergodic decomposition for T is given. This proof do not rely on profound Choquet＇s representing theorem.

关 键 词：连续变换 不变概率测度 遍历性 

分 类 号：O177.2[理学—数学]