Average pseudo-orbits and metric mean dimension with potential

Abstract

Through a measure-theoretic approach, we show that the metric mean dimension or topological pressure of a topological dynamical system with potential can be calculated by measuring the complexity of average pseudo-orbits in the induced infinite product space with respect to the potential function. This result extends several previously known conclusions related to the topological entropy (or topological pressure, upper mean dimension with potential) and pseudo-orbits in the literature.