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<p>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 measure-theoretic quantities, and establish a variational principle that connects the topological and measure-theoretic versions of the BS dimension.</p>

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On the Variational Principle for BS Dimension in Amenable Group Actions

  • 期刊论文

  • 发表日期：

    2025年6月7日

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  • Lei Liu,
  • Dongmei Peng

摘要

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 measure-theoretic quantities, and establish a variational principle that connects the topological and measure-theoretic versions of the BS dimension.