Second species periodic solutions for the three body problem

Abstract

We are going to explain the construction of second-species periodic solutions for the Restricted Planar Circular 3-Body Problem. These solutions, whose existence had been conjectured by Poincaré, are referred to periodic solutions that travel near singular points. To do that, we will study two different papers, one written by S.V.Bolotin and R.S.Mackay, and the other one written by Jean-Pierre Marco and Laurent Niederman. Although they have much in common, the first one gives a variational approach of the problem (using Lagrangian systems and the Principle of Least Action), while the other one gives a geometrical approach (defining isolated blocks and perturbative methods). We will explain and expand these approaches, to sum up with a briefly comparison between them. For their study, we will take as a reference the particular case of the Restricted 3-Body Problem corresponding to the Sun, Jupiter and an asteroid, whose singular point will be the collision between these last two bodies.