Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2

TL;DR

This paper classifies all relative equilibria in the two-body problem within hyperbolic 2-space and analyzes their stability using intrinsic Riemannian data, advancing understanding of dynamical behaviors in curved geometries.

Contribution

It provides a complete classification and stability analysis of relative equilibria in hyperbolic 2-space, using intrinsic geometric data, which is a novel approach.

Findings

Complete classification of relative equilibria

Stability conditions derived from Riemannian data

Insights into dynamics in hyperbolic geometry

Abstract

We classify and analyze the stability of all relative equilibria for the two-body problem in the hyperbolic space of dimension 2 and we formulate our results in terms of the intrinsic Riemannian data of the problem.