Periodic orbits for classical particles having complex energy
  This paper revisits earlier work on complex classical mechanics in which it was argued that when the energy of a classical particle in an analytic potential is real, the particle trajectories are closed and periodic, but that when the energy is complex, the classical trajectories are open. Here it is shown that there is a discrete set of eigencurves in the complex-energy plane for which the particle trajectories are closed and periodic. 
Alexander G. Anderson, Carl M. Bender, and Uriel I. Morone
math-ph hep-th math.MP