Hill-Clohessy-Wiltshire Equations

The simulation shows what happens when you push off lightly from a space station in a circular orbit around a planet with perfect Newtonian gravity. The space station stays at the point (0,0) while you float around it. x0, y0, vx0, and vy0 are the controls for the initial position and velocity of the ship. t is the current time, which runs forward automatically. tmax is the time at which the point resets back to time zero.
Most orbits go off in loops, but some are closed. Can you find them?