报告题目： A rescaled expansiveness for flows 报 告 人： 文晓 报告人所在单位： 北京航空航天大学 报告日期： 2020-11-24 星期二 报告时间： 14:00-15:00 报告地点： 腾讯会议 ID：852 4566 4051 报告摘要： We introduce a new version of expansiveness for flows. Let $M$ be a compact Riemannian manifold without boundary and $X$ be a $C^1$ vector field on $M$ that generates a flow $\varphi_t$ on $M$.  We call $X$ {\it rescaling expansive} on a compact invariant set $\Lambda$ of $X$ if for any $\epsilon>0$ there is $\delta>0$ such that, for any $x,y\in \Lambda$ and any time reparametrization $\theta:\mathbb{R}\to \mathbb{R}$, if $d(\varphi_t(x),\varphi_{\theta(t)}(y))\le \delta\|X(\varphi_t(x))\|$ for all $t\in \mathbb R$, then $\varphi_{\theta(t)}(y)\in \varphi_{[-\epsilon, \epsilon]}(\varphi_t(x))$ for all $t\in \mathbb R$. We prove that every multisingular hyperbolic set (singular hyperbolic set in particular) is rescaling expansive and a converse holds generically. Other definitions of expansiveness of flows and their relationships are also introduced. 本年度学院报告总序号： 295