Dynamics Seminar

Event Information Analytical tools for dynamics with singularities, including Sinai billiards
13:10 on Wednesday March 28, 2018
14:00 on Wednesday March 28, 2018
BA6183, Bahen Center, 40 St. George St.
Viviane Baladi


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. With M. Demers, we are now constructing the measure of maximal entropy for the billiard map. I will try to compare the two results (without entering in too much technical details!).