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arXiv · 2112.07425

Upper capacity entropy and packing entropy of saturated sets for amenable group actions

Xiankun Ren·Wenda Zhang·Yiwei Zhang
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Abstract

Let $(X,G)$ be a $G$-action topological system, where $G$ is a countable infinite discrete amenable group and $X$ a compact metric space. In this paper we study the upper capacity entropy and packing entropy for systems with weaker version of specification. We prove that the upper capacity always carries full entropy while there is a variational principle for packing entropy of saturated sets.

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Xiankun Ren, Wenda Zhang, Yiwei Zhang. 2021-12-14. Upper capacity entropy and packing entropy of saturated sets for amenable group actions. https://arxiv.org/abs/2112.07425

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