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题目:Some ergodic properties in Heisenberg group actions

2017/06/27 00:00 科研秘书 点击:[]

报告人:Huyi Hu(美国密歇根州立大学数学系)

时间:2017.06.28 14:30---15:30

地点:理科楼LD203

摘要:We consider a smooth Heisenberg group action on a manifold $M$, that is, a set of maps of $M$ of the form $f^ng^mh^k$, where $f$, $g$ and $h$ are $C^2$ diffeomorphisms such that $fh=hf$, $gh=hg$ and $fg=gfh$. We show that all Lyapunov exponents of $h$ are zero with respect to any probability measure invariant under $f$, $g$ and $h$. Also, if any map in the group is a codimensional one Anosov diffeomorphism, then $h^k=id$ for some integer $K$, hence, the action cannot be faithful. Some of the results can be generalized to higher dimensional Heisenberg group actions.

报告人简介:Huyi Hu从事微分动力系统与遍历论方面的研究。1993年美国获亚利桑那大学数学博士学位,现为美国密歇根州立大学数学系教授,南方科技大学访问教授。

学院联系人:周云华

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