A note on dimensional entropy for amenable group actions

Dou Dou, Ruifeng Zhang


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 \cite{ZC} and Simpson \cite{S}.


Topological entropy; dimensional entropy; amenable group; Hausdorff dimension; subshift

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