96-11 Luca Sbano, SISSA/ISAS Trieste Italia; e-mail

Non-collision periodic orbits with zero total angular momentum for the Newtonian Three-Body Problem (65K, LAtex) Jan 17, 96

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Abstract. We study the existence of a periodic orbit without collisions, with zero total angular momentum, in the planar Three-Body Problem by means of Lagrangian reduction, variational methods and local analysis of the flow.\par In a preceeding paper \cite{luca} we described a class of compact set of trajectories where to find minima for the Action-functional of the Three-Body Problem. In this paper we find critical points perturbatively in the masses, these critical points are in slightly bigger compact sets. We study a system composed of three bodies: two of them with small {\it different} masses compared with the mass of the third body. For the unperturbed problem we construct explicit solutions, which are regular critical points for the unperturbed Action-functional. These critical points can be {\it continued} for sufficiently small values of the masses. We prove the existence of periodic orbits without collisions. Moreover for the full Three-Body Problem on the manifold $J=0$ we verify the existence of critical points at "infinity" composed of a Kepler-problem and an "escaping" body.

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