Recurrent Weil-Petersson geodesic rays with non-uniquely ergodic ending   laminations
  We construct Weil-Petersson (WP) geodesic rays with minimal filling non-uniquely ergodic ending lamination which are recurrent to a compact subset of the moduli space of Riemann surfaces. This construction shows that an analogue of the Masur's criterion for Teichm\"uller geodesics does not hold for WP geodesics. 
Jeffrey Brock and Babak Modami
math.GT math.DS