Variational principles for finitely generated pseudogroup actions

Abstract

We study the thermodynamic formalism of finitely generated pseudogroups acting on compact metric spaces. We introduce the notions of topological and measure-theoretical pressures for those actions, which may not admit invariant measures. Moreover, we prove a variational principle and discuss the impact of the existence of a $G$-homogeneous probability measure. To clarify the scope of our main results and the relevance of our approach, we address several examples and list a few applications of interest.