Viviane Baladi: Analytical tools for dynamics with singularities, including Sinai billiards

Schedule

14:00-15:00 Prelcolloquium by Gerard Farré Puigallí (Room FB55, AlnaNova)

15:15-16:15 Colloquium lecture by Viviane Baladi (Room Oskar Klein, AlbaNova)

16:15-17:00 SMC social get together with refreshments 

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!).