For any N >= 2 we prove the existence of quasi-periodic orbits lying on N- dimensional invariant elliptic tori for the planetary planar (N + 1)-body problem. For small planetary masses, such orbits are close to the limiting solutions given by the N planets revolving around the sun on planar circles. The eigenvalues of the linearized secular dynamics are also computed asymptotically. The proof is based on an appropriate averaging and KAM theory which overcomes the difficulties caused by the intrinsic degeneracies of the model. For concreteness, we focus on a caricature of the outer solar system.

N-dimensional elliptic invariant tori for the planar (N+1)-body problem / L. Biasco, L. Chierchia, E. Valdinoci. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 37:5(2006), pp. 1560-1588. [10.1137/S0036141004443646]

N-dimensional elliptic invariant tori for the planar (N+1)-body problem

E. Valdinoci
Ultimo
2006

Abstract

For any N >= 2 we prove the existence of quasi-periodic orbits lying on N- dimensional invariant elliptic tori for the planetary planar (N + 1)-body problem. For small planetary masses, such orbits are close to the limiting solutions given by the N planets revolving around the sun on planar circles. The eigenvalues of the linearized secular dynamics are also computed asymptotically. The proof is based on an appropriate averaging and KAM theory which overcomes the difficulties caused by the intrinsic degeneracies of the model. For concreteness, we focus on a caricature of the outer solar system.
N-body problem; nearly integrable Hamiltonian systems; lower-dimensional elliptic tori
Settore MAT/05 - Analisi Matematica
2006
Article (author)
File in questo prodotto:
File Dimensione Formato  
s0036141004443646.pdf

accesso aperto

Tipologia: Publisher's version/PDF
Dimensione 277.71 kB
Formato Adobe PDF
277.71 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/472851
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 23
  • ???jsp.display-item.citation.isi??? 23
social impact