Geodesics on Margulis spacetimes

Abstract

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.

12 pages, no figures, to appear in the issue of "Ergodic Theory and Dynamical Systems" dedicated to the memory of Daniel Rudolph