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