### 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 language | English |
---|---|

Pages (from-to) | 1560-1588 |

Number of pages | 29 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 37 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Jan 2006 |

Externally published | Yes |

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### Cite this

*SIAM Journal on Mathematical Analysis*,

*37*(5), 1560-1588. https://doi.org/10.1137/S0036141004443646

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*SIAM Journal on Mathematical Analysis*, vol. 37, no. 5, pp. 1560-1588. https://doi.org/10.1137/S0036141004443646

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - N-dimensional elliptic invariant tori for the planar (N + 1)-body problem

AU - Biasco, Luca

AU - Chierchia, Luigi

AU - Valdinoci, Enrico

PY - 2006/1/1

Y1 - 2006/1/1

N2 - 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.

AB - 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.

KW - Lower-dimensional elliptic tori

KW - N-body problem

KW - Nearly integrable hamiltonian systems

UR - http://www.scopus.com/inward/record.url?scp=33748869744&partnerID=8YFLogxK

U2 - 10.1137/S0036141004443646

DO - 10.1137/S0036141004443646

M3 - Article

VL - 37

SP - 1560

EP - 1588

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 5

ER -