Polygonal negative hyperbolic rotopulsators of the curved $n$-body problem

Abstract

For the $n$-body problem in spaces of negative constant Gaussian curvature, we prove for a class of negative hyperbolic rotopulsators that if that class exists, the configurations of the point masses of these rotopulsators have to be regular polygons if the rotopulsators are not relative equilibria. Additionally, we prove that if the rotopulsators are relative equilibria, there exists at most one such solution.

References in corpus (5)

• Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere $S^2$ and the hyperbolic plane $H^2$
• Relative equilibria in the 3-dimensional curved n-body problem
• The classical N-body problem in the context of curved space
• All the Lagrangian relative equilibria of the curved 3-body problem have equal masses
• Existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi-homogeneous $n$-body problems and the curved $n$-body problem