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Tuesday Seminar on Topology
Seminar information archive ～04/20｜Next seminar｜Future seminars 04/21～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2019/10/08
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Masaki Tsukamoto (Kyushu University)
How can we generalize hyperbolic dynamics to group actions? (JAPANESE)
Masaki Tsukamoto (Kyushu University)
How can we generalize hyperbolic dynamics to group actions? (JAPANESE)
[ Abstract ]
Hyperbolicity is one of the most fundamental concepts in the study of dynamical systems. It provides rich (expansive and positive entropy) and yet controllable (stable and having some nice measures) dynamical systems. Then, can we generalize this to group actions?
A naive approach seems difficult. For example, suppose $Z^2$ smoothly acts on a finite dimensional compact manifold. Then it is easy to see that its entropy is zero. In other words, there is no rich $Z^2$-actions in the ordinary finite dimensional world. So we must go to infinite dimension. But what kind structure can we expect in the infinite dimensional world?
The purpose of this talk is to explain that mean dimension seems to play an important role in such a research direction. In particular, we explain the following principle :
If $Z^k$ acts on a space $X$ with some hyperbolicity, then we can control the mean dimension of the sub-action of any rank $(k-1)$ subgroup $G$ of $Z^k$.
This talk is based on the joint works with Tom Meyerovitch and Mao Shinoda.
Hyperbolicity is one of the most fundamental concepts in the study of dynamical systems. It provides rich (expansive and positive entropy) and yet controllable (stable and having some nice measures) dynamical systems. Then, can we generalize this to group actions?
A naive approach seems difficult. For example, suppose $Z^2$ smoothly acts on a finite dimensional compact manifold. Then it is easy to see that its entropy is zero. In other words, there is no rich $Z^2$-actions in the ordinary finite dimensional world. So we must go to infinite dimension. But what kind structure can we expect in the infinite dimensional world?
The purpose of this talk is to explain that mean dimension seems to play an important role in such a research direction. In particular, we explain the following principle :
If $Z^k$ acts on a space $X$ with some hyperbolicity, then we can control the mean dimension of the sub-action of any rank $(k-1)$ subgroup $G$ of $Z^k$.
This talk is based on the joint works with Tom Meyerovitch and Mao Shinoda.
