Tame and chaotic behavior in the planar isosceles 3-body problem

Diacu, F.N.

Celestial Mechanics-Dynamical Astronomy 50(4): 313-324


ISSN/ISBN: 1572-9478
Accession: 088216577

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We show that every planar isosceles solution of the three-body problem encounters a collision of the symmetric particles, either forwards or backwards in time. Regularizing analytically this collision, the solution has at least a syzygy configuration and/or leads to a total collapse. Some further simple results support the intuitive image on the tame local behavior of the motion as long as it does not lead to a triple collision. As a main result we prove that total collapse singularities, can be regularized in a C 1-fashion with respect to time, for all values of the masses. Using symbolic dynamics, the chaotic character of the C 1-regularized solutions is pointed out.