Geometric Potentials and Thermodynamic Formalism

This lecture focuses on geometric potentials and topological pressure in the context of dispersing billiard maps. The instructor introduces the concept of geometric potentials, equilibrium states, and the associated transfer operator. Key topics include the definition of topological pressure, growth lemmas, and the properties of pressure functions. The lecture also covers the spectral gap for the transfer operator, existence, and uniqueness of equilibrium states, and the analyticity of pressure functions. Various results and references in the field of thermodynamic formalism for dispersing billiards are discussed.