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

2016/08/29 by Pieter Tibboel, Tibboel, Pieter
Earth and Planetary Sciences · Physics and Astronomy · Mathematics · #Geophysics and Gravity Measurements #Nuclear physics research studies #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1608.07931

Abstract

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

Related

• On the non-existence of hyperbolic polygonal relative equilibria for the negative curved n--body problem with equal masses
• Circular non-collision orbits for a large class of n-body problems
• Existence of a class of rotopulsators
• Finiteness of polygonal relative equilibria for generalised\n quasi-homogeneous n-body problems and n-body problems in spaces of\n constant curvature
• Continuation of relative equilibria in the n--body problem to spaces\n of constant curvature