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

Research paper by Dongmei Zheng, Ercai Chen

Indexed on: 03 May '18Published on: 01 May '18Published in: Science China Mathematics


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