Pressure on non-compact spaces

Abstract: Thermodynamic formalism has a lot to say in the context of sufficiently regular dynamical systems in compact spaces, for example about the existence and uniqueness properties of equilibrium states, and their characterisation as some derivative of the pressure function. This talk considers non-compact settings, particularly the case of countable Markov shifts. A first natural approach is to take the completion of the space and hope that the boundary created doesn’t interfere with too many thermodynamic properties. I’ll look at how one might do this, some drawbacks, and how they can, in some cases, be overcome.

dynamical systems

Audience: researchers in the topic

Dynamical systems seminar at the Jagiellonian University