随机动力系统的 Weyl 平均等度连续性和 Weyl 平均敏感性

数学物理学报 ›› 2024, Vol. 44 ›› Issue (6): 1595-1606.

随机动力系统的 Weyl 平均等度连续性和 Weyl 平均敏感性

连媛^1,^*(),刘红军²(),朱斌³()

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
³重庆工商大学数学与统计学院重庆 400067

收稿日期:2024-02-21 修回日期:2024-06-11 出版日期:2024-12-26 发布日期:2024-11-22
通讯作者: ^*连媛，Email: andrea@tynu.edu.cn
作者简介:刘红军, Email:hongjunliu@gznu.edu.cn;|朱斌, Email:binzhuctbu@ctbu.edu.cn
基金资助:
山西省基础研究(202103021223322)

Weyl Mean Equicontinuity and Weyl Mean Sensitivity of A Random Dynamical System

Lian Yuan^1,^*(),Liu Hongjun²(),Zhu Bin³()

¹College of Mathematics and Statistics, Taiyuan Normal University, Shanxi Jinzhong 030619
²School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025
³School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067

Received:2024-02-21 Revised:2024-06-11 Online:2024-12-26 Published:2024-11-22
Supported by:
Fundamental Research Program of Shanxi Province(202103021223322)

摘要/Abstract

摘要：

该文首先介绍了无限可数离散顺从群作用的连续随机动力系统的 Weyl 平均等度连续性和 Weyl 平均敏感性,然后得到了当随机动力系统相应的斜积变换为极小作用时系统的 Weyl 平均等度连续性和 Weyl 平均敏感性之间具有二分法的结论.

关键词: 平均等度连续性, 平均敏感性, 随机动力系统

Abstract:

In this article, we introduce the concepts of Weyl-mean equicontinuity and Weyl-mean sensitivity of a random dynamical system associated to an infinite countable discrete amenable group action. We obtain the dichotomy result to Weyl-mean equicontinuity and Weyl-mean sensitivity of a random dynamical system when the corresponding skew product transformation is minimal.

Key words: Mean equicontinuity, Mean sensitivity, Random dynamical system

中图分类号:

O193

连媛, 刘红军, 朱斌. 随机动力系统的 Weyl 平均等度连续性和 Weyl 平均敏感性[J]. 数学物理学报, 2024, 44(6): 1595-1606.

Lian Yuan, Liu Hongjun, Zhu Bin. Weyl Mean Equicontinuity and Weyl Mean Sensitivity of A Random Dynamical System[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1595-1606.

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