Polynomial Entropy of Amenable Group Actions for Noncompact Sets  

作　　者：Lei LIU Xiao Yao ZHOU 

机构地区：[1]School of Mathematics and Statistics,Shangqiu Normal University,Shangqiu 476000,China [2]School of Mathematical Sciences and Institute of Mathematics,Nanjing Normal University,Nanjing 210023,China

出　　处：《Acta Mathematica Sinica,English Series》2023年第7期1351-1368,共18页数学学报（英文版）

基　　金：supported by Foundation in higher education institutions of He’nan Province,P. R. China(Grant No. 23A110020);National Natural Science Foundation of China (Grant No. 11401363);the Foundation for the Training of Young Key Teachers in Colleges and Universities in He’nan Province,P. R. China (Grant No.2018GGJS134);supported by National Natural Science Foundation of China (Gratn No.11971236);China Postdoctoral Science Foundation (Grant No. 2016M591873);China Postdoctoral Science Special Foundation (Grant No. 2017T100384);funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。

摘　　要：In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation between local measure-theoretic polynomial entropy of Borel probability measures and polynomial entropy on an arbitrary subset. Also, we establish a variational principle for polynomial entropy on compact subsets in the context of amenable group actions.

关 键 词：Bowen polynomial entropy local measure-theoretic polynomial entropy variational principle amenable group 

分 类 号：O19[理学—数学]