Banach Upper Density Recurrent Points of C^0-flows  

作　　者：Qi YAN Jian Dong YIN Ballesteros MARNELLIE Wei Ling WU 

机构地区：[1]Department of Mathematics,Nanchang University

出　　处：《Acta Mathematica Sinica,English Series》2016年第11期1312-1322,共11页数学学报（英文版）

基　　金：Supported by National Natural Science Foundations of China(Grant Nos.11261039,11661054);National Natural Science Foundation of Jiangxi(Grant No.20132BAB201009)

摘　　要：Let X denote a compact metric space with distance d and F ： X×R→ X or Ft ： X→X denote a C0-flow. From the point of view of ergodic theory, all important dynamical behaviors take place on a full measure set. The aim of this paper is to introduce the notion of Banach upper density recurrent points and to show that the closure of the set of all Banach upper density recurrent points equals the measure center or the minimal center of attraction for a C0-flow. Moreover, we give an example to show that the set of quasi-weakly almost periodic points can be included properly in the set of Banach upper density recurrent points, and point out that the set of Banach upper density recurrent points can be included properly in the set of recurrent points.Let X denote a compact metric space with distance d and F ： X×R→ X or Ft ： X→X denote a C0-flow. From the point of view of ergodic theory, all important dynamical behaviors take place on a full measure set. The aim of this paper is to introduce the notion of Banach upper density recurrent points and to show that the closure of the set of all Banach upper density recurrent points equals the measure center or the minimal center of attraction for a C0-flow. Moreover, we give an example to show that the set of quasi-weakly almost periodic points can be included properly in the set of Banach upper density recurrent points, and point out that the set of Banach upper density recurrent points can be included properly in the set of recurrent points.

关 键 词：C0-flow measure centre weakly almost periodic point quasi-weakly almost periodicpoint Banach upper density recurrent point 

分 类 号：O19[理学—数学]