[1]张文达,薛丽翠.自由半群作用的拓扑熵的研究[J].南京师范大学学报(自然科学版),2019,42(02):61-64.[doi:10.3969/j.issn.1001-4616.2019.02.010]
　Zhang Wenda,Xue Licui.Topological Entropy of Free Semigroup Actions[J].Journal of Nanjing Normal University(Natural Science Edition),2019,42(02):61-64.[doi:10.3969/j.issn.1001-4616.2019.02.010]
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自由半群作用的拓扑熵的研究()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第42卷
期数:
2019年02期
页码:
61-64
栏目:
·数学与计算机科学·
出版日期:
2019-06-30

文章信息/Info

Title:
Topological Entropy of Free Semigroup Actions
文章编号:
1001-4616(2019)02-0061-04
作者:
张文达1; 薛丽翠2
(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)
Author(s):
Zhang Wenda1; Xue Licui2
(1.College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China)(2.College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang 050024,China)
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
Keywords:
free semigroup action; separated set; spanning set; open cover; topological entropy; equitopological conjugate
分类号:
37A35,37B40
DOI:
10.3969/j.issn.1001-4616.2019.02.010
文献标志码:
A
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power rule性质.
Abstract:
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.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2019-02-16.
基金项目:国家自然科学基金(11501066)、重庆市教委项目(KJ1705122).
通讯联系人:张文达,博士,研究方向:动力系统. E-mail:wendazhang951@aliyun.com
更新日期/Last Update: 2019-06-30