Thermodynamic Formalism for Dispersing Billiards

This lecture covers the geometry of dispersing billiards, including the periodic Lorentz gas, the associated billiard map, and statistical properties with respect to the Sinai-Ruelle-Bowen measure. The goal is to extend the analysis to equilibrium states associated with geometric potentials. Topics include hyperbolicity, distortion control, stable and unstable cones, invariant families of curves, singularities, linear bound on complexity, and growth lemma.