A new branch of Mountain Pass solutions for the choreographical 3-body problem

We prove the existence of a new branch of solutions of Mountain Pass type for the periodic 3--body problem with choreographical constraint. At first we describe the variational structure of the action functional associated to the choreographical three body problem in $\RR^3$. In the second part, using on a bisection algorithm, we provide a numerical non-rigorous solution of Mountain Pass type for this problem in a rotating frame with angular velocity $1.5$. The last step consists in the rigorous computer-assisted proof of the existence of a full branch of solutions for the problem starting from the Mountain Pass solution detected numerically.