Variational approach to second species periodic solutions of Poincaré of the 3 body problem

Details Variational approach to second species periodic solutions of Poincaré of the 3 body problem Variational approach to second species periodic solutions of Poincaré of the 3 body problem

2011-04-12

arxiv.org/abs/1104.2288v1

Mathematics

Dynamical Systems

Scientific paper

We consider the plane 3 body problem with 2 of the masses small. Periodic solutions with near collisions of small bodies were named by Poincar\'e second species periodic solutions. Such solutions shadow chains of collision orbits of 2 uncoupled Kepler problems. Poincar\'e only sketched the proof of the existence of second species solutions. Rigorous proofs appeared much later and only for the restricted 3 body problem. We develop a variational approach to the existence of second species periodic solutions for the nonrestricted 3 body problem. As an application, we give a rigorous proof of the existence of a class of second species solutions.

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