Elliptic Islands in the Planar Circular Restricted 3-Body Problem

par Vaughn Osterman (Université du Maryland)

mercredi 5 nov. 2025, 10:30 → 12:00 Europe/Paris

Denisse (Paris)

We consider the planar circular restricted three-body problem, modeling the motion of a massless asteroid in the plane undergoing gravitational attraction toward two bodies, each of which moves in a circular path around their common center of mass. For small mass ratios, the motion of the asteroid is approximated by the Kepler system when the asteroid is far from a collision, leading to quasi-periodic motions in the region of the phase space where the paths traced by the asteroid and the smaller body do not intersect. However, in the region of the phase space where the paths do intersect, the potential for close interactions between the asteroid and the smaller body destroy these quasi-periodic motions. The existence of hyperbolic sets in which the asteroid repeatedly comes close to a collision was proven independently by Bolotin and MacKay and by Font, Nunes, and Simó. My result, currently in preparation, is that there also exist elliptic periodic orbits near Kepler orbits with resonant frequencies in which the asteroid repeatedly undergoes close interactions with the smaller body. Furthermore, these elliptic periodic orbits are surrounded by elliptic islands, and the total measure of the elliptic islands in the phase space is bounded below by a positive constant.