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“Analytical tools for dynamics with singularities,including Sinai billiards “

Date:

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Time:

Wednesday, 23. Nov 2017

Video-Recording for any system with MP4-support

- Video.mp4 (ca.354 Mb)

15:15 – 16:15

Speaker: Viviane Baladi, (Institut de Mathématiques de Jussieu - Paris Rive Gauche, France)

Location: Oskar Klein, Albanova

Abstract :

In the past 15 years, tools from analysis, in particular new Banach spaces of anisotropic

distributions on manifolds, have allowed substantial progress in dynamical systems.

After briefly explaining how a spectral gap for a transfer operator furnishes ergodic

information, I shall focus on Sinai billiards maps and flows. These natural but technically

challenging systems are uniformly hyperbolic and volume preserving - however grazing

orbits give rise to singularities. New analytic tools allowed us (with M. Demers and

C. Liverani) to obtain exponential mixing for the natural volume and finite horizon Sinai

billiard flows. More recently (with M. Demers), we constructed the measure of maximal

entropy for the billiard map. I will try to compare the two results (without entering in too

much technical details!).