Topological Methods in Nonlinear Analysis

A note on dimensional entropy for amenable group actions

Dou Dou and Ruifeng Zhang

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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 Følner sequences; the Hausdorff dimension of an amenable subshift (for certain metric associated to some Følner sequence) equals its topological entropy. This answers questions by Zheng and Chen [10] and Simpson [9].

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Topol. Methods Nonlinear Anal., Volume 51, Number 2 (2018), 599-608.

First available in Project Euclid: 24 April 2018

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Dou, Dou; Zhang, Ruifeng. A note on dimensional entropy for amenable group actions. Topol. Methods Nonlinear Anal. 51 (2018), no. 2, 599--608. doi:10.12775/TMNA.2017.056.

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