Chaotic dynamics for the two body problem on a sphere

TL;DR

This paper proves the existence of chaotic trajectories in the two-body problem on a sphere, using advanced mathematical methods to demonstrate complex dynamics similar to classical three-body solutions.

Contribution

It introduces a novel application of the anti-integrable limit method to Lagrangian systems with Newtonian singularities on a spherical surface.

Findings

Existence of chaotic trajectories near collisions

Trajectories resemble second species solutions of Poincaré

Method applicable to systems with Newtonian singularities

Abstract

We prove the existence of chaotic trajectories for the two body problem on a sphere. The trajectories we construct encounter near-collisions and are similar to the second species solutions of Poincar\'e of the classical 3 body problem. The construction uses a general result on Lagrangian systems with Newtonian singularities of the potential which is based on the method of anti-integrable limit of Serge Aubry.