Thermodynamic formalism for coarse expanding dynamical systems

This lecture explores the thermodynamic formalism for weakly coarse expanding dynamical systems, focusing on equilibrium states, visual metrics, and symbolic coding. It discusses recent developments in expanding Thurston maps and the construction of equilibrium states for these maps. The lecture also covers the concept of coarse expanding conformal systems and the existence of the measure of maximal entropy. Additionally, it delves into the construction of coding trees and the almost injective nature of the coding. Theoretical results such as the Central Limit Theorem, Law of Iterated Logarithm, and Large Deviations are presented, along with the application of these concepts in establishing statistical laws for weakly coarse expanding systems.