Quasi periodic co-orbital motions (joint work with Philippe Robutel and Alexandre Pousse)

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 (hence stable) which exhibit this exchange property in the three body plane planetary problem thanks to KAM theory.
[1] On the Co-orbital Motion in the Three-Body Problem: Existence of Quasi-periodic Horseshoe-Shaped Orbits, L. Niederman, A. Pousse, P. Robutel, Comm. Math. Phys., vol. 377, pp. 551–612 (2020)