Variational principle for weighted amenable topological pressure

2023/06/27 by Yang Jiao, Yang, Jiao, Ercai Chen +5
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2306.15509

openalex publication_date 2023/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 [Ergodic Theory Dynam. Syst. 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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