Approximate solutions of cohomological equations associated with some Anosov flows

The Livshitz theorem reported in 1971 asserts that any C 1 function having zero integrals over all periodic orbits of a topologically transitive Anosov flow is a derivative of another C 1 function in the direction of the flow. Similar results for functions of higher differentiability have also appeared since. In this paper we prove a “finite version“of the Livshitz theorem for a certain class of Anosov flows on 3-dimensional manifolds which include geodesic flows on negatively curved surfaces as a special case.