  We prove topological transitivity for the Weil Petersson geodesic flow for
two-dimensional moduli spaces of hyperbolic structures. Our proof follows a new
approach that exploits the density of singular unit tangent vectors, the
geometry of cusps and convexity properties of negative curvature. We also show
that the Weil Petersson geodesic flow has: horseshoes, invariant sets with
positive topological entropy, and that there are infinitely many hyperbolic
closed geodesics, whose number grows exponentially in length. Furthermore, we
note that the volume entropy is infinite.
