Dynamical intricacy and average sample complexity of amenable group actions

作     者：Jie Li Siming Tu Jie Li;Siming Tu

作者机构：School of Mathematics and StatisticsJiangsu Normal UniversityXuzhou 221116China School of Mathematics(Zhuhai)Sun Yat-sen UniversityZhuhai 519082China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2022年第65卷第6期

页      面：1247-1266页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11701231) supported by National Natural Science Foundation of China(Grant Nos.11801584 and 11871228) National Science Foundation of Jiangsu Province(Grant No.BK20170225) Science Foundation of Jiangsu Normal University(Grant No.17XLR011) 

主　　题：intricacy average sample complexity topological entropy amenable group 

摘      要：In 2018,Petersen and Wilson introduced the notion of dynamical intricacy and average sample complexity for dynamical systems of Z-action,based on the past works on the notion of intricacy in the research of brain network and probability *** one wants to take into account underlying system geometry in applications,more general group actions may need to be taken into *** this paper,we consider this notion in the case of amenable group *** show that many basic properties in the Z-action case remain *** also show that their suprema over covers or partitions are equal to the amenable topological entropy and the measure entropy,using the quasitiling technique in the theory of the amenable group.