Classification of positive elliptic-elliptic rotopulsators on Clifford tori

2020/11/30 by Pieter Tibboel, Tibboel, Pieter
Physics and Astronomy · Mathematics · #Astro and Planetary Science #Nuclear physics research studies #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2011.14539

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.

Related

• Positive elliptic-elliptic rotopulsators on Clifford tori of nonconstant\n size project onto regular polygons
• Existence of a class of rotopulsators
• Polygonal negative hyperbolic rotopulsators of the curved n-body\n problem
• Circular non-collision orbits for a large class of n-body problems
• Rotationally invariant constant Gauss curvature surfaces in Berger\n spheres