Measure-theoretic pressure and topological pressure in mean metrics

Abstract

ABSTRACTIn this paper, using spanning sets in mean metrics we construct a new definition of measure-theoretic pressure of ergodic measures over a topological dynamical system. And we establish a pressure version of Katok's entropy formula in the case of mean metrics. Furthermore, we also introduce a new definition of topological pressure by replacing the Bowen metrics with the corresponding mean metrics, and prove that the new topological pressure is equivalent to the classical topological pressure. Then the variational principle for the newly defined topological pressure is obtained.