RELATIVE ENTROPY DIMENSION FOR COUNTABLE AMENABLE GROUP ACTIONS  

作　　者：肖祖彪 殷正宇 Zubiao XIAO;Zhengyu YIN(School of Mathematics and Statistics,Fuzhou University,Fuzhou 350116,China;Department of Mathematics,Nanjing University,Nanjing 210093,China)

机构地区：[1]School of Mathematics and Statistics,Fuzhou University,Fuzhou 350116,China [2]Department of Mathematics,Nanjing University,Nanjing 210093,China

出　　处：《Acta Mathematica Scientia》2023年第6期2430-2448,共19页数学物理学报（B辑英文版）

基　　金：supported by the NNSF of China (12201120,12171233);the Educational Research Project for Young and Middle-aged Teachers of Fujian Province (JAT200045).

摘　　要：We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups.First,for a given Følner sequence,we define the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity.we also investigate the relations among these.Second,we introduce the notion of a relative dimension set.Moreover,using the method,we discuss the disjointness between the relative entropy zero extensions via the relative dimension sets of two extensions,which says that if the relative dimension sets of two extensions are different,then the extensions are disjoint.

关 键 词：amenable groups relative entropy dimensions relative dimension sets 

分 类 号：O19[理学—数学]