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• 天元讲堂（6.21）：A rescaled expansiveness for flows
• 浏览量：261 发布人：佚名 发布时间：2017-06-13 12:18:06
• 报告题目：A rescaled expansiveness for flows I

报告人 文晓（北京航天航空大学）

报告时间 2017年6月21日09:30-10:30

报告地点  维格堂319

报告摘要 In this talk, I will introduce a new version of expansiveness for $C^1$ vector fields as following: a $C^1$ vector field $X$ will be called {\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 $d(\varphi_t(x), \varphi_{\theta(t)}(y)\leq \delta\|X(\varphi_t(x))\|$ for all $t\in \mathbb R$, then $\varphi_{\theta(t)}(y)\in \varphi_{(-\epsilon, \epsilon)}(\varphi_t(x))$ for all $t\in \mathbb R$. Then I'll show several equivalent definitions for this rescaled expansiveness similar to the Bowen-Walters' expansiveness for nonsingular flows.

报告题目：A rescaled expansiveness for flows II

报告人 文晓（北京航天航空大学）

报告时间 2017年6月21日10:30-11:30

报告地点  维格堂319

报告摘要 In this talk， I will show that every multisingular hyperbolic set (singular hyperbolic set in particular) is rescaling expansive and a converse holds generically. Here the multisingular hyperbolicity is a notion recently introduced by Bonatti-da Luz which well characterize the notion of star flows.