Breakdown of homoclinic connection to L3 and chaotic coorbital motions in the Restricted Planar Circular 3-Body Problem

par M. Marcel Guardia (Universitat Politècnica de Catalunya)

jeudi 24 mars 2022, 14:30 → 16:30 Europe/Paris

Observatoire de Paris, Salle Danjon

Abstract: Consider the Restricted Planar Circular 3-Body Problem (RPC3BP) with small mass ratio mu. The RPC3BP, in rotating coordinates, possesses five equilibrium points, among them the so called L3 which is collinear with the primaries and beyond the largest one. The point L3 is a saddle center equilibrium and has 1-dimensional stable and unstable manifolds. In this talk, we will present an asymptotic formula for the distance between the stable and unstable manifolds of L3 for small mu. This distance is exponentially small with respect to mu and, therefore, classical perturbative methods do not apply. We will also analyze the (possible) intersections of the invariant manifolds of the Lyapunov periodic orbits emanating from L3. This will lead to the existence of chaotic coorbital motions and also to homoclinic tangencies. This is a joint work with Inma Baldomá and Mar Giralt.