On the convergence of an algorithm constructing the normal form for lower dimensional elliptic tori in planetary systems
Articolo
Data di Pubblicazione:
2014
Citazione:
On the convergence of an algorithm constructing the normal form for lower dimensional elliptic tori in planetary systems / A. Giorgilli, U. Locatelli, M. Sansottera. - In: CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY. - ISSN 0923-2958. - 119:3-4(2014 Aug), pp. 397-397. [10.1007/s10569-014-9562-7]
Abstract:
We give a constructive proof of the existence of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov's normalization algorithm to the case of planetary systems, for which elliptic tori may be used as replacements of elliptic keplerian orbits in Lagrange-Laplace theory. With this paper we support with rigorous convergence estimates the semi-analytical work in our previous article (2011), where an explicit calculation of an invariant torus for a planar model of the Sun-Jupiter-Saturn-Uranus system has been made. With respect to previous works on the same subject we exploit the characteristic of Lie series giving a precise control of all terms generated by our algorithm. This allows us to slightly relax the non-resonance conditions on the frequencies.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Hamiltonian systems; KAM theory; Lie series; Lower dimensional invariant tori; n-Body planetary problem; Normal form methods; Small divisors
Elenco autori:
A. Giorgilli, U. Locatelli, M. Sansottera
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