Families of symmetric periodic orbits in the three body problem and the figure eight

In this paper we show a technique for the continuation of symmetric periodic orbits in systems with time-reversal symmetries. The geometric idea of this technique allows us to generalize the “cylinder” theorem for this kind of systems. We state the main theoretical result without proof (to be published elsewhere). We focus on the application of this scheme to the three body problem (TBP), taking as starting point the figure eight orbit [3] to find families of symmetric periodic orbits.