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

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.

arXiv comment27 pages, 7 figures

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Cited by in corpus (10)

• Reduction and relative equilibria for the 2-body problem in spaces of constant curvature
• Relative equilibria for the positive curved $n-$body problem
• Bifurcations of the Lagrangian orbits from the classical to the curved 3-body problem
• Central configurations of the curved $N$-body problem
• The $N$-Body Problem in Spaces with Uniformly Varying Curvature
• Singular Reduction of the 2-Body Problem on the 3-Sphere and the 4-Dimensional Spinning Top
• Choreography solutions of the $n$-body problem on $S^2$
• Compactness and index of ordinary central configurations for the curved n-body problem
• Attracting and repelling 2-body problems on a family of surfaces of constant curvature
• The Asymptotic Structure of the Centred Hyperbolic 2-Monopole Moduli Space