Global Secular Dynamics in the Planar Three-Body Problem
Féjoz, Jacques (2002), Global Secular Dynamics in the Planar Three-Body Problem, Celestial Mechanics and Dynamical Astronomy, 84, 2, p. 159-195. http://dx.doi.org/10.1023/A:1019969024779
TypeArticle accepté pour publication ou publié
Journal nameCelestial Mechanics and Dynamical Astronomy
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Abstract (EN)We use the global construction which was made in [6, 7] of the secular systems of the planar three-body problem, with regularized double inner collisions. These normal forms describe the slow deformations of the Keplerian ellipses which each of the bodies would describe if it underwent the universal attraction of only one fictitious other body. They are parametrized by the masses and the semi-major axes of the bodies and are completely integrable on a fixed transversally Cantor set of the parameter space. We study this global integrable dynamics reduced by the symmetry of rotation and determine its bifurcation diagram when the semi-major axes ratio is small enough. In particular it is shown that there are some new secular hyperbolic or elliptic singularities, some of which do not belong to the subset of aligned ellipses. The bifurcation diagram may be used to prove the existence of some new families of 2-, 3- or 4-frequency quasiperiodic motions in the planar three-body problem , as well as some drift orbits in the planar n-body problem .
Subjects / Keywordsthree-body problem; secular system; averaging; KAM theorem; regularization; singularity
Showing items related by title and author.
Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem Féjoz, Jacques; Guardia, Marcel; Kaloshin, Vadim; Roldán, Pablo (2016) Article accepté pour publication ou publié