Periodic orbits for classical particles having complex energy

This Letter 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.

► This Letter presents new previously unknown periodic complex-energy solutions.
► Until this work it was thought that all complex-energy solutions were nonperiodic.
► The new periodic solutions are a set of measure 0 of all complex-energy solutions.
► However, they are crucial because they are dense in the set of all solutions.