David Parmenter

Constructing equilibrium states for some hyperbolic systems

The aim of the talk is to describe a new construction of equilibrium states for certain hyperbolic systems using unstable manifolds. We will provide an introduction to the study of thermodynamic formalism and in particular the importance of equilibrium states. Then we will explore the known constructions of equilibrium states in the setting of hyperbolic systems including the Sinai-Ruelle-Bowen measure and look at how our new construction fits into the picture. Finishing with a discussion of the future directions of exploration in this area.