Jacques FEJOZ

Astronomie et Systèmes Dynamiques
Bureau des Longitudes
77 avenue Denfert-Rochereau
75014 Paris
fejoz@bdl.fr

Isotropic Invariant Tori in the Planar Three-Body Problem

Abstract : I have studied the secular system of the planar three body problem when the ratio of the semi major axes is small. It is a completely integrable hamiltonian system on the \(2\)-sphere. It has the prominent role in the way the disturbing function pertubs the \(2\)-frequency degenerate keplerian motion.

Indeed, in the (non averaged) three body problem, a positive measure of regular points of the secular system gives rise to Lagrangian invariant \(4\)-tori. On the other hand a positive measure of non degenerate singular points of the secular system gives rise to isotropic invariant \(3\)-tori. So, these tori have intermediate dimension between Lagrangian tori and degenerate Keplerian tori, and their normal dynamics is elliptic or hyperbolic. The proof relies on Herman's versions of isotropic invariant tori theorems.