Scale pressure for amenable group actions

Abstract

In this paper we introduce the notion of scale pressure and measure theoretic scale pressure for amenable group actions. A variational principle for amenable group actions is presented. We also describe these quantities by pseudo-orbits. Moreover, we prove that if $G$ is a finitely generated countable discrete amenable group, then the scale pressure of $G$ coincides with the scale pressure of $G$ with respect to pseudo-orbits.