TY - JOUR T1 - Periodic orbits close to elliptic tori and applications to the three-body problem JF - Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004) 87-138 Y1 - 2004 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Enrico Valdinoci AB - We prove, under suitable non-resonance and non-degeneracy ``twist\\\'\\\' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of Hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses of the ``planets\\\'\\\'. The proofs are based on averaging theory, KAM theory and variational methods. (Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential Equations.) PB - Scuola Normale Superiore di Pisa UR - http://hdl.handle.net/1963/2985 U1 - 1348 U2 - Mathematics U3 - Functional Analysis and Applications ER -