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.
Titolo: | $N$-dimensional elliptic invariant tori for the planar $(N+1)$-body problem |
Autori: | |
Data di pubblicazione: | 2006 |
Rivista: | |
Citazione: | 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. |
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. |
Handle: | http://hdl.handle.net/11590/139629 |
Appare nelle tipologie: | 1.1 Articolo in rivista |