Periodic orbits close to elliptic tori and applications to the three-body problem

2003/04/08 by Massimiliano Berti, Luca Biasco, Berti, Massimiliano +3
Mathematics · Physics and Astronomy · #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Nuclear physics research studies #Quantum chaos and dynamical systems #math.DS

paper · pdf · doi:10.48550/arxiv.math/0304103

arxiv created 2003/04/08 · openalex publication_date 2003/04/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.)

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