Gibbs measures on compact ultra metric spaces

2022/02/14 by C. -E. Pfister, Pfister, C. -E.
Mathematics · #37B10 #37C85 #37D20 #37D35 #82B05 #82B20 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2202.06802

openalex publication_date 2022/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One proves the equivalence of a Gibbs measure and a Gibbs conformal measure for a dynamical system (G,X) when G is a countably infinite discrete group acting expansively on a compact ultrametric space X. As an application one proves for any beta-shift, that the unique equilibrium measure for a function of summable variation is a Gibbs measure.

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