Yakov Pesin: Thermodynamics of the Katok Map

Abstract: I will describe the smooth non-uniformly hyperbolic map of the two dimensional torus known as the Katok map. It is a slowdown of a linear Anosov automorphism near the origin and it is a local (but not small) perturbation. The Katok map was the first example of the area preserving diffeomorphism with non-zero Lyapunov exponents and can be used to construct such diffeomorphisms on any surface. I will then discuss the thermodynamical formalism for the Katok map, i.e., demonstrate existence and uniqueness of equilibrium measures associated with the geometric potential and their ergodic properties including decay of correlations and the Central Limit Theorem. This is based on recent works with S. Senti and K. Zhang.