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
@article{ASNSP_2004_5_3_1_87_0, author = {Berti, Massimiliano and Biasco, Luca and Valdinoci, Enrico}, title = {Periodic orbits close to elliptic tori and applications to the three-body problem}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {87--138}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 3}, number = {1}, year = {2004}, mrnumber = {2064969}, zbl = {1121.37047}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2004_5_3_1_87_0/} }
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 SP - 87 EP - 138 VL - 3 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2004_5_3_1_87_0/ LA - en ID - ASNSP_2004_5_3_1_87_0 ER -
%0 Journal Article %A Berti, Massimiliano %A Biasco, Luca %A Valdinoci, Enrico %T Periodic orbits close to elliptic tori and applications to the three-body problem %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2004 %P 87-138 %V 3 %N 1 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2004_5_3_1_87_0/ %G en %F ASNSP_2004_5_3_1_87_0
Berti, Massimiliano; Biasco, Luca; 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, Serie 5, Volume 3 (2004) no. 1, pp. 87-138. http://archive.numdam.org/item/ASNSP_2004_5_3_1_87_0/
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