顺从群作用系统中一扩充映射的熵

数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 359-365.

顺从群作用系统中一扩充映射的熵

连媛¹^,^*(), 刘红军²

¹太原师范学院数学与统计学院山西晋中 030619
²贵州师范大学数学科学学院贵阳 550025

收稿日期:2025-03-04 修回日期:2025-07-19 出版日期:2026-02-26 发布日期:2026-01-19
通讯作者: 连媛 E-mail:andrea@tynu.edu.cn
基金资助:
国家自然科学基金(12461012);山西省基础研究项目(20210302123322)

An Entropy of an Extended Map of Amenable Group Actions

Yuan Lian¹^,^*(), Hongjun Liu²

¹College of Mathematics and Statistics, Taiyuan Normal University, Shanxi Jinzhong 030619
²School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025

Received:2025-03-04 Revised:2025-07-19 Online:2026-02-26 Published:2026-01-19
Contact: Yuan Lian E-mail:andrea@tynu.edu.cn
Supported by:
NSFC(12461012);Fundamental Research Program of Shanxi Province(20210302123322)

摘要/Abstract

摘要：

研究拓扑空间上群作用和相应的熵理论在数学物理学和拓扑学中都是非常重要的. 因子映射是研究保测动力系统结构理论的一个关键概念, 而条件熵定量地刻画了因子映射的复杂性. 该文计算了顺从群作用动力系统中一类扩充映射的条件熵, 其数值为零.

关键词: 熵, 动力系统, 群作用, 顺从群, 扩充映射

Abstract:

The study of group actions and the corresponding entropy theory in topological spaces is very important in mathematical physics and topology. Factor map is a key concept in the study of the structural theory of measure preserving dynamical systems. Conditional entropy, on the other hand, quantitatively characterises the complexity of factor map. In this paper, we calculate the conditional entropy of a class of extended maps in the dynamical system for amenable group actions, and its value is zero.

Key words: entropy, dynamical system, group action, amenable group, extended map

中图分类号:

O193

连媛, 刘红军. 顺从群作用系统中一扩充映射的熵[J]. 数学物理学报, 2026, 46(1): 359-365.

Yuan Lian, Hongjun Liu. An Entropy of an Extended Map of Amenable Group Actions[J]. Acta mathematica scientia,Series A, 2026, 46(1): 359-365.

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