A note on dimensional entropy for amenable group actions
Dynamical Systems
2017-12-19 v1
Abstract
In this short note, for countably infinite amenable group actions, we provide topological proofs for the following results: Bowen topological entropy (dimensional entropy) of the whole space equals the usual topological entropy along tempered F{\o}lner sequences; the Hausdorff dimension of an amenable subshift (for certain metric associated to some F{\o}lner sequence) equals its topological entropy. This answers questions by Zheng and Chen (Israel Journal of Mathematics 212 (2016), 895-911) and Simpson (Theory Comput. Syst. 56 (2015), 527-543).
Cite
@article{arxiv.1712.06152,
title = {A note on dimensional entropy for amenable group actions},
author = {Dou Dou and Ruifeng Zhang},
journal= {arXiv preprint arXiv:1712.06152},
year = {2017}
}