A local conditional variational principle of pressures and local conditional equilibrium states

Abstract

In this article, we introduce the notions of topological conditional pressures and two measure-theoretical conditional pressures of a finite open cover conditioned by a fixed finite measurable partition. We establish a local conditional variational principle and show that local conditional pressures determine local conditional measure-theoretical entropies. As applications, we study properties of both local and global conditional equilibrium states for continuous, real-valued functions.