Special Session 15: Geometric and variational techniques in the N-body problem
Contents
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.
It is generally accepted that Poincar\'e's arguments do not
provide a 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. It turns out that Poincar\'e's proof is essentially
correct. The talk is based on a work with Piero Negrini.