Classification of positive elliptic-elliptic rotopulsators on Clifford tori

TL;DR

This paper classifies positive elliptic-elliptic rotopulsator solutions in curved spaces, showing they either lie on great circles or project onto regular polygons with equal masses, and confirms their existence.

Contribution

It provides a complete classification of positive elliptic-elliptic rotopulsators on Clifford tori in curved spaces, including existence results.

Findings

Solutions lie on great circles or project onto regular polygons

All masses are equal in polygon-projection solutions

Existence of these rotopulsator solutions is established

Abstract

We prove that positive elliptic-elliptic rotopulsator solutions of the $n$-body problem in spaces of constant Gaussian curvature that move on Clifford tori of nonconstant size either lie on great circles, or project onto regular polygons. We additionally prove for the case that the configurations project onto regular polygons that all masses are equal and show that all these different types of positive elliptic-elliptic rotopulsator exist.