Geodesics on Margulis spacetimes
  Let M be a Margulis spacetime whose associated complete hyperbolic surface S has compact convex core. Generalizing the correspondence between closed geodesics on M and closed geodesics on S, we establish an orbit equivalence between recurrent spacelike geodesics on M and recurrent geodesics on S. In contrast, no timelike geodesic recurs in either forward or backwards time. 
William M. Goldman and Francois Labourie
math.DS math.DG