天元讲堂（6.21）：A rescaled expansiveness for flows
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.
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.