Abstract (EN)

In the direct product of the phase and parameter spaces, we de ne the perturbing region, where the Hamiltonian of the planar three-body problem is Ck-close to the dynamically degenerate Hamiltonian of two uncoupled two-body problems. In this region, the secular systems are the normal forms that one gets by trying to eliminate the mean anomalies from the perturbing function. They are Pöschel-integrable on a transversally Cantor set. This construction is the starting point for proving the existence of and describing several new families of periodic or quasiperiodic orbits: short periodic orbits associated to some secular singularities, which generalize Poincaré's periodic orbits of the second kind (\Les Méthodes nouvelles de la mécanique céleste", Fi rst Vol., Gauthiers-Villars, Paris, 1892{1899); quasiperiodic motions with three (resp. two) frequencies in a rotating frame of reference, which generalize Arnold's solutions (Russian Math. Survey 18 (1963), 85{191) (resp. Lieberman's solu- tions; Celestial Mech. 3 (1971), 408{426); and three-frequency quasiperiodic motions along which the two inner bodies get arbitrarily close to one another an in nite number of times, generalizing the Chenciner-Llibre's invariant "punc- tured tori" (Ergodic Theory Dynamical Systems 8 (1988), 63{72). The proof relies on a sophisticated version of kam theorem, which itself is proved using a normal form theorem of M. Herman ("Démonstration d'un Théorème de V.I. Arnold," Séminaire de Systèmes Dynamiques and Manuscipts, 1998).