2022/07/05 by Yang, Rui, Chen, Ercai, Zhou, Xiaoyao · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2207.01901
Borrowing the idea of topological pressure determining measure-theoretical entropy in topological dynamical systems, we establish a variational principle for upper metric mean dimension with potential in terms of upper measure-theoretical metric mean dimension of invariant measures. Moreover, the notion of equilibrium state is introduced to characterize these measures that attain the supremum of the variational principle.