Using Inönü-Wigner Lie-algebra contraction and a local slice on the cotangent bundle, non-degenerate relative equilibria and relative periodic orbits of general Hamiltonian systems persist from the Euclidean plane to spheres and hyperbolic planes of constant curvature, with application to the n-body
Martínez, C.Sim\'o Relative equilibria of the restricted three-body problem in curved spaces, Celestial Mechanics and Dynamical Astronomy 128, No
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Continuation of Hamiltonian dynamics from the plane to constant-curvature surfaces
Using Inönü-Wigner Lie-algebra contraction and a local slice on the cotangent bundle, non-degenerate relative equilibria and relative periodic orbits of general Hamiltonian systems persist from the Euclidean plane to spheres and hyperbolic planes of constant curvature, with application to the n-body