KAM tori for \(n\)-body problems: a brief history

DOI10.1007/s10569-005-6215-xzbMath1152.70008OpenAlexW2058078171MaRDI QIDQ850674

Luigi Chierchia, Alessandra Celletti

Publication date: 6 November 2006

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

Full work available at URL: https://doi.org/10.1007/s10569-005-6215-x

zbMATH Keywords

KAM theoryInvariant toriComputer-assisted proofsSmall divisor problems

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical systems in classical and celestial mechanics (37N05) (n)-body problems (70F10) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) History of mechanics of particles and systems (70-03)

Related Items (11)

Regular and singular reductions in the spatial three-body problem ⋮ Determination of the doubly symmetric periodic orbits in the restricted three-body problem and Hill's lunar problem ⋮ A cartographic study of the phase space of the elliptic restricted three body problem. Application to the Sun-Jupiter-asteroid system ⋮ Nonlinear dynamical analysis for displaced orbits above a planet ⋮ The planetary \(N\)-body problem: symplectic foliation, reductions and invariant tori ⋮ A Window into the World of KAM Theory ⋮ Displaced orbits generated by solar sails for the hyperbolic and degenerated cases ⋮ Measures of basins of attraction in spin-orbit dynamics ⋮ Analytic intermediate dimensional elliptic tori for the planetary many-body problem ⋮ The eccentric frame decomposition of central force fields ⋮ Lissajous and halo orbits in the restricted three-body problem

Cites Work

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