For any $Ngeq 2$ 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/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.

Biasco, L., Chierchia, L., Valdinoci, E. (2006). $N$-dimensional elliptic invariant tori for the planar $(N+1)$-body problem. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 37, 1560-1588.

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

BIASCO, LUCA;CHIERCHIA, Luigi;
2006-01-01

Abstract

For any $Ngeq 2$ 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/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.
Biasco, L., Chierchia, L., Valdinoci, E. (2006). $N$-dimensional elliptic invariant tori for the planar $(N+1)$-body problem. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 37, 1560-1588.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/139629
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