自由半群作用的拓扑熵的研究  

Topological Entropy of Free Semigroup Actions

作　　者：张文达 薛丽翠[2] Zhang Wenda;Xue Licui(College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China;College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074 [2]河北师范大学信息与计算机科学学院,河北石家庄050024

出　　处：《南京师大学报（自然科学版）》2019年第2期61-64,共4页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11501066);重庆市教委项目(KJ1705122)

摘　　要：本文给出了三种自由半群作用的动力系统的拓扑熵的定义,首先证明了这三种定义的等价性.在此定义的基础上对拓扑熵性质进行了讨论.主要包括以下结论:在等度拓扑共轭下拓扑熵的不变性以及这种拓扑熵的powerrule性质.In this paper,we define the entropy and preimage entropy of free semigroup actions in a new method. Based on these definitions,we get some relations between topological entropy and measure entropy,and the relations among kinds of preimage entropies. The main results of this paper are as follows:(1)The topological entropy is invariant under equi- conjugacy;(2)The power rule for the measure-theoretic entropy holds.

关 键 词：自由半群作用 生成集 分离集 开覆盖 拓扑熵 等度拓扑共轭 

分 类 号：O152[理学—数学]