Topological Pressure for sub-additive potentials of amenable group actions

TL;DR

This paper introduces a new way to measure the complexity of group actions using topological pressure for sub-additive potentials, establishing a local variational principle for this measure.

Contribution

It defines topological pressure for sub-additive potentials in amenable group actions and proves a local variational principle, extending existing thermodynamic formalism.

Findings

Defined topological pressure for sub-additive potentials

Established a local variational principle

Extended thermodynamic formalism to amenable group actions

Abstract

We define the topological pressure for any sub-additive potentials of the countable discrete amenable group action and any given open cover. A local variational principle for the topological pressure is established.