Abstract

Regularity properties of the pressure are related to phase transitions. In this article we study thermodynamic formalism for sys- tems defined in non-compact phase spaces, our main focus being count- able Markov shifts. We produce metric compactifications of the space which allow us to prove that the pressure is differentiable on a residual set and outside an Aronszajn null set in the space of uniformly continu- ous functions. We establish a criterion, the so called sectorially arranged property, which implies that the pressure in the original system and in the compactification coincide. Examples showing that the compactifica- tions can have rich boundaries, for example a Cantor set, are provided