THE SYSTEMS WITH ALMOST BANACH-MEAN EQUICONTINUITY FOR ABELIAN GROUP ACTIONS  

作　　者：Bin ZHU Xiaojun HUANG Yuan LIAN 朱斌;黄小军;连媛(College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China;Chongqing Key Laboratory of Analytic Mathematics and Applications,Chongqing University,Chongqing 401331,China;Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China [2]Chongqing Key Laboratory of Analytic Mathematics and Applications,Chongqing University,Chongqing 401331,China [3]Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China

出　　处：《Acta Mathematica Scientia》2022年第3期919-940,共22页数学物理学报（B辑英文版）

基　　金：supported by NSF of China(11671057);NSF of Chongqing(cstc2020jcyj-msxmX0694);the Fundamental Research Funds for the Central Universities(2018CDQYST0023).

摘　　要：In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain that the topological entropy of a transitive,almost Banach-mean equicontinuous dynamical system of Abelian group action is zero.As an application of our main result,we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.

关 键 词：Abelian group action Banach mean equicontinuous Banach mean density independence set 

分 类 号：O152[理学—数学]