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

• Massimiliano Berti ^[1] ; Luca Biasco ^[2] ; Enrico Valdinoci ^[3]
  1. [1] International School for Advanced Studies

     International School for Advanced Studies

     Trieste, Italia

     
  2. [2] Università Roma Tre, Italy
  3. [3] Università di Roma Tor Vergata, Italy

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 3, Nº 1, 2004, págs. 87-138
• Idioma: inglés
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• Resumen

  • 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.