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Tuesday Seminar on Topology
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2011/05/31
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Takehiko Morita (Osaka University)
Measures with maximum total exponent and generic properties of $C^
{1}$ expanding maps (JAPANESE)
Takehiko Morita (Osaka University)
Measures with maximum total exponent and generic properties of $C^
{1}$ expanding maps (JAPANESE)
[ Abstract ]
This is a joint work with Yusuke Tokunaga. Let $M$ be an $N$
dimensional compact connected smooth Riemannian manifold without
boundary and let $\\mathcal{E}^{r}(M,M)$ be the space of $C^{r}$
expandig maps endowed with $C^{r}$ topology. We show that
each of the following properties for element $T$ in $\\mathcal{E}
^{1}(M,M)$ is generic.
\\begin{itemize}
\\item[(1)] $T$ has a unique measure with maximum total exponent.
\\item[(2)] Any measure with maximum total exponent for $T$ has
zero entropy.
\\item[(3)] Any measure with maximum total exponent for $T$ is
fully supported.
\\end{itemize}
On the contrary, we show that for $r\\ge 2$, a generic element
in $\\mathcal{E}^{r}(M,M)$ has no fully supported measures with
maximum total exponent.
This is a joint work with Yusuke Tokunaga. Let $M$ be an $N$
dimensional compact connected smooth Riemannian manifold without
boundary and let $\\mathcal{E}^{r}(M,M)$ be the space of $C^{r}$
expandig maps endowed with $C^{r}$ topology. We show that
each of the following properties for element $T$ in $\\mathcal{E}
^{1}(M,M)$ is generic.
\\begin{itemize}
\\item[(1)] $T$ has a unique measure with maximum total exponent.
\\item[(2)] Any measure with maximum total exponent for $T$ has
zero entropy.
\\item[(3)] Any measure with maximum total exponent for $T$ is
fully supported.
\\end{itemize}
On the contrary, we show that for $r\\ge 2$, a generic element
in $\\mathcal{E}^{r}(M,M)$ has no fully supported measures with
maximum total exponent.
