当前位置: X-MOL 学术J. Differ. Equ. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On mean sensitive tuples
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2021-06-28 , DOI: 10.1016/j.jde.2021.06.032
Jie Li , Tao Yu

In this paper we introduce and study several mean forms of sensitive tuples. It is shown that the topological or measure-theoretical entropy tuples are correspondingly mean sensitive tuples under certain conditions (minimal in the topological setting or ergodic in the measure-theoretical setting). Characterizations of the question when every non-diagonal tuple is mean sensitive are presented. Among other results we show that under minimality assumption a topological dynamical system is weakly mixing if and only if every non-diagonal tuple is mean sensitive and so as a consequence every minimal weakly mixing topological dynamical system is mean n-sensitive for any integer n2. Moreover, the notion of weakly sensitive in the mean tuple is introduced and it turns out that this property has some special lift property. As an application we obtain that the maximal mean equicontinuous factor for any topological dynamical system can be induced by the smallest closed invariant equivalence relation containing all weakly sensitive in the mean pairs.



中文翻译:

在平均敏感元组上

在本文中,我们介绍并研究了敏感元组的几种均值形式。结果表明,拓扑或测度理论熵元组在某些条件下(在拓扑设置中最小或在测度理论设置中遍历)相应地是平均敏感元组。当每个非对角元组对均值敏感时问题的特征被呈现。在其他结果中,我们表明,在极小假设下,拓扑动力系统弱混合当且仅当每个非对角元组都是均值敏感的,因此,每个最小弱混合拓扑动力系统对任何整数都是均值n敏感的n2. 此外,引入了均值元组中弱敏感的概念,结果表明该属性具有一些特殊的提升属性。作为一个应用,我们获得了任何拓扑动力系统的最大平均等连续因子可以由包含均值对中所有弱敏感的最小闭合不变等价关系引起。

更新日期:2021-06-28
down
wechat
bug