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arXiv · 1712.06152

A note on dimensional entropy for amenable group actions

Dou Dou·Ruifeng Zhang
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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).

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Dou Dou, Ruifeng Zhang. 2017-12-17. A note on dimensional entropy for amenable group actions. https://arxiv.org/abs/1712.06152

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