Martingale method and geodesic flow on a surface of negative constant curvature

Let ((TS)-S-1, m, (T-t)(t is an element ofR)) be the geodesic flow on the u nit tangent bundle of a surface S of negative constant curvature and finite volume. We show that every Holder function on (TS)-S-1 is, for the discret e time action of the geodesic flow, homologous to a martingale increment. F rom this representation follow the central limit theorem and its improvemen ts, and a characterization of Holder functions which are coboundaries in th e class of measurable functions.