94-386 Luca Sbano, SISSA/ISAS Trieste Italia; e-mail [email protected]

On the lack of coercivity of the reduced Action-functional for zero total angular momentum in the planar Newtonian three-body problem (57K, LAtex) Dec 4, 94

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Abstract. Combining hamiltonian reduction, variational methods and local analysis of the flow, we study for the planar three-body problem, the existence of non trivial periodic orbit without collisions, with zero total angular momentum. We prove that collision solutions are not minima, but the lack of compactness for the sub-levels of the Action-functional does not allow to prove the existence of $T$-periodic orbits without collisions. We restrict therefore to study periodic solutions which are odd under reflection (thorough some axis which may depend on the orbit). In this setting we prove that the loss of compactness is due to trajectories which are asymptotically collinear and we identify a class of sets which are compact and which are good candidates for the search of a minimum. (In the fonts there are some AMStex fonts)

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