We prove topological transitivity for the Weil-Petersson geodesic flow for real two-dimensional moduli spaces of hyperbolic structures. Our proof follows a new approach that combines 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.
All Science Journal Classification (ASJC) codes