具有弱specification性质的amenable群作用的拟弱几乎周期点的回复层次  

Recurrent Levels of Quasi-weakly Almost Periodic Points of Amenable Group Actions with the Specification Property

作　　者：周亚婷 尹建东[1] ZHOU Yating;YIN Jiandong(School of Mathematics and Computer Sciences,Nanchang University,Nanchang,Jiangxi,330031,P.R.China)

机构地区：[1]南昌大学数学与计算机学院,江西南昌330031

出　　处：《数学进展》2023年第5期945-954,共10页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.12061043)

摘　　要：设(X,G)是一个G-系统,{F_(n)}_(n=1)^(∞)是G的一个Fϕlner序列.本文证明了如果(X,G)具有强specification性质,则在(X,G)上存在一个相对于G的Fϕlner序列{F_(n)}_(n=1)^(∞)的真拟弱几乎周期点x和一个由x沿着{F_(n)}_(n=1)^(∞)的轨道生成的不变测度μ,使得μ的支撑与x的相对于Fϕlner序列{F_(n)}_(n=1)^(∞)的极小吸引中心相同.此外,如果(X,G)有弱specification性质且(X,G)的周期测度在(X,G)的不变测度集合M(X,G)中稠密,则在(X,G)上存在一个相对于G上的Fϕlner序列{F_(n)}_(n=1)^(∞)的真拟弱几乎周期点y,使得每一个由y的轨道沿Fϕlner序列{F_(n)}_(n=1)^(∞)生成的不变测度v的支撑与点y相对于{F_(n)}_(n=1)^(∞)的极小吸引中心不相等.Let(X,G)be a G-system and{F_(n)}_(n=1)^(∞)be a Fϕlner sequence of G.In this paper,we prove that if(X,G)has the strong specification property,then there exist a proper quasi-weakly almost periodic point x relative to the Fϕlner sequence{F_(n)}_(n=1)^(∞)of G in(X,G)and an invariant measureμgenerated by the orbit of x along{F_(n)}_(n=1)^(∞)such that the support ofμis equal to the minimal center of attraction relative to the Fϕlner sequence{F_(n)}_(n=1)^(∞)of x.In addition,if(X,G)has the weak specification property and the set of periodic measures of(X,G)is dense in the set of invariant measures M(X,G)of(X,G),then there exists a proper quasi-weakly almost periodic point y relative to the Fϕlner sequence{F_(n)}_(n=1)^(∞)of G in(X,G)such that the support of each invariant measure v generated by the orbit of y along the Fϕlner sequence{F_(n)}_(n=1)^(∞)is not equal to the minimal center of attraction relative to{F_(n)}_(n=1)^(∞)of y.

关 键 词：specification性质 不变测度 amenable群作用 真拟弱几乎周期点 

分 类 号：O194[理学—数学]