Existence and uniqueness of equilibrium states for systems with specification at a fixed scale: an improved Climenhaga–Thompson criterion*

Abstract

Abstract We consider the uniqueness of equilibrium states for dynamical systems that satisfy certain weak, non-uniform versions of specification, expansivity, and the Bowen property at a fixed scale. Following Climenhaga–Thompson’s approach which was originally due to Bowen and Franco, we prove that equilibrium states are unique even when the weak specification assumption only holds on a small collection of orbit segments. This improvement will be crucial in a subsequent work, where we will prove that (open and densely) every Lorenz attractor supports a unique measure of maximal entropy.