Central forces depending on the distance only. Case where all the bounded orbits are periodic

It is shown in this paper that the only potentials corresponding to central force for which all the bounded orbits are periodic are the potential of the harmonic oscillator and of the two body problem. A discussion is given in the case where a circular orbit exists and when the orbits near the circular orbit are periodic.We calculate in these cases the angle between pericentre and apocentre.Celestial Mechanics