Periodic orbits of the N-body problem with the symmetry of platonic polyhedra

Abstract

We review some recently discovered periodic orbits of the N-body problem [8], whose existence is proved bymeans of variational methods. These orbits are minimizers of the Lagrangian action functional in a set of T-periodic loops, equivariant for the action of a group G and satisfying some topological constraints. Both the group action and the topological constraints are defined using the symmetry of Platonic polyhedra.