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

TL;DR

This paper demonstrates the existence of infinite symmetric periodic solutions in the planar Newtonian n-body problem using variational methods and symmetry constraints, with some results supported numerically.

Contribution

It introduces a novel approach to find symmetric periodic orbits in the n-body problem by minimizing a discretized action functional under symmetry constraints.

Findings

Existence of infinite families of symmetric periodic solutions.

Solutions are supported by numerical evidence under strong-force assumptions.

Method applies to positive masses in the planar Newtonian n-body problem.

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.