Abstract: An invariant probability measure for a dynamical system is physical if there exists a set with positive Lebesgue measure of points whose forward orbits equidistribute towards the measure. Proving the existence of such a measure is a major problem. Marcelo Viana has conjectured that a smooth diffeomorphism admits a physical measure if the Lyapunov exponents of its orbits in a full volume set do not vanish. I will explain how a technique controlling the continuity of Lyapunov exponents allows to prove this conjecture in the case of smooth surface diffeomorphisms. This is a joint work with Jérôme Buzzi and Omri Sarig.
Biography: Sylvain Crovisier is directeur de recherches at the Centre National de la Recherche Scientifique (CNRS) and works at the Laboratoire de mathématiques d’Orsay (Université Paris-Saclay). His research deals with topological and differential dynamical systems, their perturbations and their ergodic theory. He was invited at the International Congress of the Mathematicians 2014 in Seoul.