报告题目: Shortest distance between two orbits of a dynamical system
报告人：廖灵敏(武汉大学)
报告时间：2022年9月29日10:00-10:50
报告地点：腾讯会议：625-541-561
会议密码请邮件咨询yangdw@vnsclub.net
报告摘要：Let $(X, T, \mu)$ be a measure-preserving dynamical system, where the space $X$ is equipped with a
metric $d$. For two points $ x, y \in X$, and a positive integer $n$, define $m_n (x, y)$ as the shortest distance
between the orbit points $T^i x$ and $T^j y$ with $0 \leq i , j \leq n-1$.
It is proved that under certain rapid mixing conditions of the dynamical system,$\mu \times \mu$-almost surely $ -\log m_n (x, y) / \log n $ converges to the constant $2 / C_{\mu}$, where $C_{\mu}$ is the correlation dimension of the measure $\mu$.
It is also proved that for the case of irrational rotations, where the irrationality exponent of the angle of rotation is much involved, the behavior of $ -\log m_n (x, y) / \log n $ is quite different.
This is a joint work with Vanessa Barros and Jérôme Rousseau.
邀请人：杨大伟