*S peaker.* Sylvain Crovisier

*Date.*11.10.22 at 2:00 pm

* Abstrac*t. I will explain a relation between the discontinuities of the Lyapunov exponents and of the entropy, with respect to the invariant measures of smooth diffeomorphisms of surfaces. Among the consequences, one gets an answer to a conjecture by Viana on surfaces: if the Lyapunov exponents are positive for a set with positive area, there exists an SRB measure. This is a joint work with J. Buzzi and O. Sarig.