Uniqueness of central foliations of geodesic flows for compact surfaces without conjugate points

Abstract

We show that the only continuous, codimension one foliations which are invariant under the action of the geodesic flow of a compact surface without conjugate points are the central stable and the central unstable foliations. The uniqueness of central foliations as the only invariant, codimension one foliations is typical of Anosov systems and expansive geodesic flows in compact manifolds without conjugate points. We generalize this result to geodesic flows in compact surfaces without conjugate points with no further assumptions on the dynamics of the flow.