Dynamical Resistance Day

Stronger ergodic properties for equilibrium states in non-positive curvature
20 de Novembro | 11h00min | Daniel Thompson (The Ohio State University, USA)

Title: Stronger ergodic properties for equilibrium states in non-positive curvature (video)

Equilibrium states for geodesic flows over compact rank 1 non-positive curvature manifolds and sufficiently regular potential functions were studied by Burns, Climenhaga, Fisher and myself. We showed that if the higher rank set does not carry full topological pressure then the equilibrium state is unique. In this talk, I will describe some recent results on the dynamical properties of these unique equilibrium states. We show that these equilibrium states have the Kolmogorov property (joint with Ben Call), and that approximations of the equilibrium states by regular closed geodesics asymptotically satisfy a type of Central Limit Theorem (joint with Tianyu Wang). Time permitting, I will explain some of the main ideas behind the proofs, focusing on the MME case to ease the exposition.