报告时间：2020年12月1日（星期二）下午3:30

地点：工西416 学术报告厅

摘要：Let $(X,T)$ be a topological dynamical system with metric $d$. We define a new function $\overline{F}(x,y)=\limsup\limits_{n \to +\infty} \inf\limits_{\sigma \in S_n} \frac 1n \sum\limits_{k=1}^n d(T^k x,T^{\sigma(k)} y)$ by using permutation group $S_n$. It's shown $F(x,y)=\lim\limits_{n \to +\infty} \inf\limits_{\sigma \in S_n} \frac 1n \sum\limits_{k=1}^n d(T^k x,T^{\sigma(k)} y)$ exists when $x,y \in X$ are generic points.

Applying this function, we prove $(X,T)$ is uniquely ergodic if and only if $\overline{F}(x,y)=0$ for any $x,y \in X$. The characterizations of ergodic measures and physical measures by $\overline{F}(x,y)$ are given. We introduce the notion of weak mean equicontinuity and prove that $(X,T)$ is weak mean equicontinuous if and only if the time averages $f^{*}(x)=\lim\limits_{n \to +\infty}\frac 1n \sum\limits_{k=1}^n f(T^k x)$ are continuous for all $f \in C(X)$.

报告人简介：郑立奇，2020年6月博士毕业于中国科学院数学与系统科学研究院，2020年7月开始在中国科学技术大学从事博士后工作，研究方向为拓扑动力系统与遍历理论研究，论文发表在J. Diff. Equ.等期刊。