Topological entropy of sets of generic points for actions of amenable groups

Abstract

Let $G$ be a countable discrete amenable group which acts continuously on a compact metric space $X$ and let $\mu$ be an ergodic $G-$invariant Borel probability measure on $X$. For a fixed tempered Følner sequence $\{F_n\}$ in $G$ with $\underset{n\to +\infty }{\lim }\frac{|F_n|}{\log n}=\infty$, we prove the following variational principle: $$h^B(G_{\mu },\{F_n\})=h_{\mu }(X,G),$$ where $G_{\mu }$ is the set of generic points for $\mu$ with respect to $\{F_n\}$ and $h^B(G_{\mu },\{F_n\})$ is the Bowen topological entropy (along $\{F_n\}$) on $G_{\mu }$. This generalizes the classical result of Bowen in 1973.

Science China Mathematics, 2017

References in corpus (1)

• Bowen entropy for actions of amenable groups

Cited by in corpus (4)

• Bowen's equations for upper metric mean dimension with potential
• Variational principles for topological pressures on subsets
• Packing topological entropy for amenable group actions
• Bowen entropy of generic point for fixed-point free flows