Uniqueness of equilibrium states for Lorenz attractors in any dimension

Abstract

In this note, we consider the thermodynamic formalism for Lorenz attractors of flows in any dimension. Under a mild condition on the H\"older continuous potential function $\phi$, we prove that for an open and dense subset of $C^1$ vector fields, every Lorenz attractor supports a unique equilibrium state. In particular, we obtain the uniqueness for the measure of maximal entropy.