Topological Pressure and the Variational Principle of Noncompact Sets for Amenable Group Actions

TL;DR

This paper extends the concept of topological pressure and establishes a variational principle for noncompact sets under amenable group actions, broadening the theoretical framework in dynamical systems.

Contribution

It introduces a variational principle for topological pressure on noncompact sets for amenable group actions under the tempered condition, advancing the understanding of dynamical invariants.

Findings

Established the variational principle for noncompact sets

Extended topological pressure concepts to amenable group actions

Demonstrated the importance of the tempered condition

Abstract

The notion of topological pressure was introduced by Ruell and also he formulated a variational principle for the topological pressure. Pesin and Pitskel introduced a definition of topological on subsets inspired by Hausdorff dimension. In this paper, we considered the topological pressure of a noncompact subset for amenable group actions and showed that under the tempered condition, we get the variational principle for topological pressure.