Dynamical Systems SeminarFriday September 20th, 2019 Time: 2:30 PM - 3:30 PM Title: Flexibility of Lyapunov exponents with respect to two classes of measures on the torus Speaker: Alena Erchenko, Stony Brook University Location: Math Tower P-131 Abstract: We consider a family of Anosov area-preserving diffeomorphisms on the two-torus that are homotopic to a fixed Anosov automorphism. There are several interesting classes of invariant measures. We will concentrate on the invariant measure that is absolutely continuous with respect to the Lebesgue measure and the measure of maximal entropy. We show that positive Lyapunov exponents with respect to these two probability measures in the considered family of diffeomorphisms take on all values that satisfy some well-known inequalities.