abstract: The motions of the satellites Janus and Epimetheus around Saturn are among the most intriguing in the solar system since they exchange their orbits every four years. In 1, we give a rigorous proof of the existence of quasi-periodic orbits of this kind in the three body plane planetary problem thanks to KAM theory. We will discuss extensions of these results to get lagrangian tori in the same problem.
Ref: On the co-orbital motion in the three-body problem: existence of quasi-periodic horseshoe-shaped orbits, arXiv 1806.07262