Equilibrium States Through Potential Theory - Lecture 1

Explore the concept of equilibrium states in thermodynamic formalism through this lecture by Fabrizio Bianchi from Université de Lille. Delve into a recent construction of equilibrium states for rational maps and endomorphisms of P^k(C) in any dimension, based on (pluri)potential theory. Discover how this approach establishes the existence, uniqueness, and fine statistical properties of equilibrium states for general continuous functions, including Hölder ones. Learn about the central role of equilibrium states as invariant measures that maximize the pressure functional, depending on a given function φ, and understand their relationship to the measure of maximal entropy. This 1 hour and 39 minute talk, part of the Simons Semester on Dynamics, offers an in-depth exploration of potential theory's application in studying equilibrium states for complex dynamical systems.