A note on dimensional entropy for amenable group actions
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 Flner sequences; the Hausdorff dimension of an amenable subshift (for certain metric associated to some Flner 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).
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