Tail variational principle and asymptotic $h$-expansiveness for amenable group actions

TL;DR

This paper extends the tail variational principle to actions of countable amenable groups, enabling new characterizations of asymptotic h-expansiveness beyond traditional integer actions.

Contribution

It introduces the tail variational principle for amenable group actions and broadens the understanding of asymptotic h-expansiveness in this context.

Findings

Proved the tail variational principle for countable amenable group actions

Extended characterizations of asymptotic h-expansiveness to these actions

Provided a framework for analyzing entropy in more general group actions

Abstract

In this paper we prove the tail variational principle for actions of countable amenable groups. This allows us to extend some characterizations of asymptotic $h$-expansiveness from $\mathbb{Z}$-actions to actions of countable amenable groups.