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

Luca Biasco, Luigi Chierchia, Enrico Valdinoci

Research output: Contribution to journalArticle

20 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1560-1588
Number of pages29
JournalSIAM Journal on Mathematical Analysis
Volume37
Issue number5
DOIs
Publication statusPublished - 1 Jan 2006
Externally publishedYes

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Invariant Tori
Orbits
Averaging Theory
KAM Theory
Solar system
Planets
Sun
Periodic Orbits
Torus
Circle
Limiting
Orbit
Eigenvalue
Invariant
Model

Cite this

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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.",
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N-dimensional elliptic invariant tori for the planar (N + 1)-body problem. / Biasco, Luca; Chierchia, Luigi; Valdinoci, Enrico.

In: SIAM Journal on Mathematical Analysis, Vol. 37, No. 5, 01.01.2006, p. 1560-1588.

Research output: Contribution to journalArticle

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AU - Valdinoci, Enrico

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