Global Secular Dynamics in the Planar Three-Body Problem

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...

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Bibliographic Details
Published in:Celestial mechanics and dynamical astronomy 2002-10, Vol.84 (2), p.159-195
Main Author: Fejoz, Jacques
Format: Article
Language:English
Subjects:
Astronomy
Collisions
Dynamical Systems
Mathematical analysis
Mathematics
Studies
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Summary: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 [7], as well as some drift orbits in the planar n-body problem [8].[PUBLICATION ABSTRACT]
ISSN:0923-2958
1572-9478
DOI:10.1023/A:1019969024779