Topological pressure for geodesic flows

We give a Riemannian formula for the topological pressure of the geodesic f low of a closed Riemannian manifold, As a consequence, we derive an asympto tic formula for the stable norm in cohomology in terms of geodesic area for manifolds with topological entropy h(top) = 0. We introduce a Poincare ser ies also in terms of geodesic arcs and we show that it defines a holomorphi c function on the half plane given by those complex numbers with real part > h(top). (C) 2000 Editions scientifiques et medicales Elsevier SAS.