Platonic Polyhedra, Topological Constraints and Periodic Solutions of the Classical $N$-Body Problem

G. Fusco, G. F. Gronchi, P. Negrini

We prove the existence of a number of smooth periodic motions $u_{\ast }$ of the classical Newtonian $N$-body problem which, up to a relabeling of the $N$ particles, are invariant under…