Equilibrium States Through Potential Theory - Lecture 2

Equilibrium States Through Potential Theory - Lecture 2

Explore the concept of equilibrium states in thermodynamic formalism through this 1 hour 32 minute 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. Gain insights into how equilibrium states maximize the pressure functional and serve as a generalization of the measure of maximal entropy. Enhance your understanding of this central concept in dynamical systems as part of the Simons Semester on Dynamics series.