Analyticity of the Sinai-Ruelle-Bowen measure for a class of simple Anosov flows

We consider perturbations of the Hamiltonian flow associated with the geodesic flow on a surface with constant negative curvature. We prove that, under a small perturbation, not necessarily of Hamiltonian character, the Sinai-Ruelle-Bowen measure associated with the flow exists and is analytic in the strength of the perturbation. An explicit example of “thermostated” dissipative dynamics is considered.