Scale pressure for amenable group actions

TL;DR

This paper introduces the concepts of scale pressure and measure theoretic scale pressure for amenable group actions, establishing a variational principle and relating these quantities to pseudo-orbits, especially for finitely generated groups.

Contribution

It presents the first definitions of scale pressure for amenable group actions and proves a variational principle linking these pressures to pseudo-orbits.

Findings

Scale pressure and measure theoretic scale pressure are introduced for amenable group actions.

A variational principle relating these pressures is established.

For finitely generated groups, scale pressure coincides with that of pseudo-orbits.

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.