A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems

DOI10.1007/s10569-011-9375-xzbMath1266.70033arXiv1010.2617OpenAlexW2049743308MaRDI QIDQ2376775

Antonio Giorgilli, Marco Sansottera, Ugo Locatelli

Publication date: 24 June 2013

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.2617

zbMATH Keywords

Hamiltonian systemsKAM theory\(n\)-body planetary problemnormal-form methodslower-dimensional invariant tori

Mathematics Subject Classification ID

Celestial mechanics (70F15) Nearly integrable Hamiltonian systems, KAM theory (70H08) Normal forms for nonlinear problems in mechanics (70K45)

Related Items (15)

Elliptic tori in FPU non-linear chains with a small number of nodes ⋮ Normal form for lower dimensional elliptic tori in Hamiltonian systems ⋮ High-order normal form stability estimates for co-orbital motion ⋮ Rigorous estimates for the relegation algorithm ⋮ On the extension of the Laplace-Lagrange secular theory to order two in the masses for extrasolar systems ⋮ Kolmogorov variation: Kam with knobs \textit{(à la Kolmogorov)} ⋮ Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability in the light of Kolmogorov and Nekhoroshev theories ⋮ On the continuation of degenerate periodic orbits via normal form: full dimensional resonant tori ⋮ On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori ⋮ Low-dimensional \(q\)-tori in FPU lattices: dynamics and localization properties ⋮ On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems ⋮ Resonant Laplace-Lagrange theory for extrasolar systems in mean-motion resonance ⋮ Quasi-periodic motions in a special class of dynamical equations with dissipative effects: a pair of detection methods ⋮ Global structure of regular tori in a generic 4D symplectic map ⋮ Continuation of spatially localized periodic solutions in discrete NLS lattices via normal forms

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