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Measures with maximum total exponent of $C^1$ diffeomorphisms with basic sets

Hold Date 2014-04-25 16:00~2014-04-25 17:30

Place Seminar Room 3, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Yusuke TOKUNAGA (Osaka University)

For a diffeomorphism on a compact manifold, we can define measure with maximum total exponent. We show that any $C^1$-diffeomorphism with basic set has a $C^1$-neighborhood satisfying the following properties. A generic element in the neighborhood has a unique measure with maximum total exponent which is of zero entropy and fully supported on the continuation of the basic set. To the contrary, we show that for $r\geq 2$ any $C^r$-diffeomorphism with basic set does not have a $C^r$-neighborhood satisfying the above properties.

This seminar is combined with Probability Seminar.