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We consider perturbations of the Hamiltonian flow associated with thegeodesic flow on a surface of constant negative curvature. We prove that, undera small perturbation, not necessarely of Hamiltonian character, the SRB measureassociated to the flow exists and is analytic in the strength of theperturbation. An explicit example of "thermostatted" dissipative dynamics isconstructed.Comment: 23 pages, corrected typo

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