Symmetric periodic orbits for the n-body problem: some preliminary results

Abstract

We show the existence of some infinite families of periodic solutions of the planar Newtonian n-body problem --with positive masses-- which are symmetric with respect to suitable actions of finite groups (under a strong--force assumption, or just numerically). The method is by minimizing a discretization of the action functional under symmetry constraints.

LaTeX file, 16 pages, 10 figures