Lipschitz Continuity and Formulas of the Gradient Vector of the SRB Entropy Functional

Abstract: The Sobolev embedding theorem implies that the SRB entropy functional is also differentiable in the family of Anosov diffeomorphisms equipped with a suitable Hilbert manifold structure. The same holds true for the SRB entropy functional over the family of smooth expanding maps on a closed Riemannian manifold. This implication leads to the local existence of the gradient flow of the SRB entropy and an explicit formula for the gradient vector of the entropy functional via the linear response of the SRB measure.