Resumen de On the Variational Principle for BS Dimension in Amenable Group Actions

Lei Liu, Dongmei Peng

• 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.