# American Institute of Mathematical Sciences

March  2021, 20(3): 1091-1102. doi: 10.3934/cpaa.2021008

## Scale pressure for amenable group actions

 School of Mathematics, Northwest University, Xi'an, 710127, China

* Corresponding author

Received  July 2020 Revised  November 2020 Published  March 2021 Early access  January 2021

Fund Project: The third author is supported by NSFC (No.11871394), and Natural Science Foundation of Shaanxi Province (2020JC-39)

In this paper we introduce the notion of scale pressure and measure theoretic scale pressure for amenable group actions. A variational principle for amenable group actions is presented. We also describe these quantities by pseudo-orbits. Moreover, we prove that if $G$ is a finitely generated countable discrete amenable group, then the scale pressure of $G$ coincides with the scale pressure of $G$ with respect to pseudo-orbits.

Citation: Dandan Cheng, Qian Hao, Zhiming Li. Scale pressure for amenable group actions. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1091-1102. doi: 10.3934/cpaa.2021008
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