On the Variational Principle for BS Dimension in Amenable Group Actions

Lei Liu; Dongmei Peng

Ayuda

On the Variational Principle for BS Dimension in Amenable Group Actions

Lei Liu ^[1] ; Dongmei Peng ^[2]
1. [1] Shangqiu Normal University
  
  Shangqiu Normal University
  
  China
2. [2] Nanjing Normal University
  
  Nanjing Normal University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 3, 2025
Idioma: inglés
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Resumen
- In this paper, we introduce and study the BS (Barreira-Schmeling) dimension for amenable group actions. Building on the thermodynamic formalism and dimension theory, we define a notion of BS dimension using Følner sequences and establish its foundational properties, including a Bowen pressure formula. Furthermore, we prove a Billingsley type theorem characterizing the BS dimension in terms of measuretheoretic quantities, and establish a variational principle that connects the topological and measure-theoretic versions of the BS dimension.
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