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

Massimiliano Berti[1]; Luca Biasco[2]; Enrico Valdinoci[3]

  • [1] Settore di Analisi Funzionale e Applicazioni Scuola Internazionale Superiore di Studi Avanzati (SISSA) Via Beirut 2-4 34014 Trieste (Italy)
  • [2] Dipartimento di Matematica Università “Roma Tre”, Largo S. L. Murialdo 1 00146 Roma (Italy)
  • [3] Dipartimento di Matematica Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma (Italy)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2004)

  • Volume: 3, Issue: 1, page 87-138
  • ISSN: 0391-173X

Abstract

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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

How to cite

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Berti, Massimiliano, Biasco, Luca, and Valdinoci, Enrico. "Periodic orbits close to elliptic tori and applications to the three-body problem." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.1 (2004): 87-138. <http://eudml.org/doc/84530>.

@article{Berti2004,
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},
affiliation = {Settore di Analisi Funzionale e Applicazioni Scuola Internazionale Superiore di Studi Avanzati (SISSA) Via Beirut 2-4 34014 Trieste (Italy); Dipartimento di Matematica Università “Roma Tre”, Largo S. L. Murialdo 1 00146 Roma (Italy); Dipartimento di Matematica Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma (Italy)},
author = {Berti, Massimiliano, Biasco, Luca, Valdinoci, Enrico},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {87-138},
publisher = {Scuola Normale Superiore, Pisa},
title = {Periodic orbits close to elliptic tori and applications to the three-body problem},
url = {http://eudml.org/doc/84530},
volume = {3},
year = {2004},
}

TY - JOUR
AU - Berti, Massimiliano
AU - Biasco, Luca
AU - Valdinoci, Enrico
TI - Periodic orbits close to elliptic tori and applications to the three-body problem
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2004
PB - Scuola Normale Superiore, Pisa
VL - 3
IS - 1
SP - 87
EP - 138
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
LA - eng
UR - http://eudml.org/doc/84530
ER -

References

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