**Title:** Thermodynamic Formalism for Sinai Billiards

**Speaker:** Mark Demers – Fairfield University

**Abstract:** While the ergodic properties of Sinai billiards with respect to the SRB measure are well understood, there have been few studies of other invariant measures and equilibrium states. As a step in this direction, we study the family of geometric potentials $– t \log (J^uT)$, $t>0$. For any finite horizon Sinai billiard map $T$, we find $t_* >1$ such that for each $t \in (0, t_*)$, there exists a unique equilibrium state $\mu_t$ for the potential. We show that $\mu_t$ is exponentially mixing for H\”older observables, and that the pressure function $P(t)$ is analytic on $(0,t_*)$. This extends our recent results for the case $t=0$, corresponding to the measure of maximal entropy. This is joint work with Viviane Baladi.