Analyticity of the SRB measure for a class of simple Anosov flows
  We consider perturbations of the Hamiltonian flow associated with the geodesic flow on a surface of constant negative curvature. We prove that, under a small perturbation, not necessarely of Hamiltonian character, the SRB measure associated to the flow exists and is analytic in the strength of the perturbation. An explicit example of "thermostatted" dissipative dynamics is constructed. 
A. Amaricci, F.Bonetto, P.Falco