Periodic orbits in elliptical galaxies. II - Rotation about the axis of symmetry

The investigation of periodic orbits in rotating oblate and prolate elliptical galaxies reveals three families of orbits at resonances; the trajectories are circular epicycles or circles in the equatorial plane coupled with vertical oscillations. They are continuations of two families of periodic orbits found in the non rotating case. The epicyclic orbits bifurcate with direct circular ones at, and do not exist beyond, a maximum angular velocity of rotation. The three families also exist outside resonances. An additional integral of motion is found.