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arXiv · 2306.15509

Variational principle for weighted amenable topological pressure

Jiao Yang·Ercai Chen·Rui Yang·Xiaoyi Yang
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Abstract

This paper aims to investigate the thermodynamic formalism of weighted amenable topological pressure for factor maps of amenable group actions. Following the approach of Tsukamoto [\emph{Ergodic Theory Dynam. Syst.} \textbf{43}(2023), 1004-1034.], we introduce the notion of weighted amenable topological pressure for factor maps of amenable group actions, and establish a variational principle for it. As the application of variational principle, we show weighted amenable measure-theoretic entropy can be determined by weighted amenable topological pressure. Equilibrium states of weighted topological pressure are also involved.

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Jiao Yang, Ercai Chen, Rui Yang, Xiaoyi Yang. 2023-06-27. Variational principle for weighted amenable topological pressure. https://arxiv.org/abs/2306.15509

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