The Multi-sensitivity and Topological Sequence Entropy of Dynamical System with Group Action

作     者：Xiao Jun HUANG Bin ZHU Xiao Jun HUANG;Bin ZHU

作者机构：College of Mathematics and StatisticsChongqing UniversityChongqing 401331P.R.China Chongqing Key Laboratory of Analytic Mathematics and ApplicationsChongqing UniversityChongqing 401331P R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2023年第39卷第4期

页      面：663-684页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 071101[理学-系统理论] 

基　　金：Supported by NSF of China (Grant No.11671057) NSF of Chongqing (Grant No.cstc2020jcyj-msxm X0694) 

主　　题：Group action multi-sensitivity topological sequence entropy hyperspace induced system 

摘      要：In this paper,we study the relationship between the multi-sensitivity and the topological maximal sequence entropy of dynamical systems for general group ***,we also discuss the consistency of multi-sensitivity of a dynamical system(G■X)and its hyperspace dynamical system G■K(X).Moreover,we research the relationship between the multi-sensitivity of two dynamical systems and the multi-sensitivity of their product space dynamical ***,we prove that if the topological sequence entropy of G■X vanishes,then so does that of its induced system G■M(X);if the topological sequence entropy of G■X is positive,then that of its induced system G■M(X)is infinity.