Upper metric mean dimension with potential for amenable group actions
Volume 280 / 2025
Studia Mathematica 280 (2025), 269-304
MSC: Primary 37A35; Secondary 37C85
DOI: 10.4064/sm240320-24-9
Published online: 5 February 2025
Abstract
A variational principle between amenable upper metric mean dimension with potential and amenable upper measure-theoretical metric mean dimension is established. The equilibrium states for the former are investigated. After introducing the notions of amenable induced upper metric mean dimension with potential on the whole space, Bowen upper metric mean dimension, and $u$-upper metric mean dimension with potential on any subset, global and local versions of Bowen’s equation are presented. Moreover, we introduce the notions of BS metric mean dimension and BS packing metric mean dimension for amenable group actions, and the corresponding variational principle and Bowen’s equations are also established.
