Analytic Lagrangian tori for the planetary many-body problem

In 2004, Féjoz[Démonstration du thorme dArnold sur la stabilit du systme plantaire (daprs M.Herman). Ergod. Th. & Dynam. Sys. 24(5) (2004), 15211582], completing investigations of Hermans [Dmonstration dun thorme de V.I. Arnold. Sminaire de Systmes Dynamiques et manuscripts, 1998], gave a complete proof of Arnolds Theorem [V.I.Arnold. Small denominators and problems of stability of motion in classical and celestial mechanics.UspekhiMat. Nauk.18(6(114)) (1963), 91192] on the planetary many-body problem, establishing, in particular, the existence of a positive measure set of smooth (C ^∞) Lagrangian invariant tori for the planetary many-body problem. Here, using Rmanns 2001 KAM theory [H.Rmann. Invariant tori in non-degenerate nearly integrable Hamiltonian systems. R. & C. Dynamics 2(6) (2001), 119203], we prove the above result in the real-analytic class.