A note on dimensional entropy for amenable group actions
Słowa kluczowe
Topological entropy, dimensional entropy, amenable group, Hausdorff dimension, subshiftAbstrakt
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}.Bibliografia
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D. Zheng and E. Chen, Bowen entropy for actions of amenable groups, Israel J. Math. 212 (2016), no. 2, 895–911.
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