Regularization of the Kepler problem on the Sphere

Abstract

In this paper we regularize the Kepler problem on $S^3$ in several different ways. First, we perform a Moser-type regularization. Then, we adapt the Ligon-Schaaf regularization to our problem. Finally, we show that the Moser regularization and the Ligon-Schaaf map we obtained can be understood as the composition of the corresponding maps for the Kepler problem in Euclidean space and the gnomonic transformation.

References in corpus (3)

• Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere $S^2$ and the hyperbolic plane $H^2$
• Levi-Civita regularization and geodesic flows for the `curved' Kepler problem
• Block regularization of the Kepler problem on surfaces of revolution with positive constant curvature