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Regularization of the Kepler Problem on the Three-sphere

  Published:2012-12-29
 Printed: Aug 2014
  • Shengda Hu,
    Department of Mathematics Wilfrid Laurier University 75 University Avenue West, Waterloo Ontario, Canada, N2L 3C5
  • Manuele Santoprete,
    Department of Mathematics Wilfrid Laurier University 75 University Avenue West, Waterloo Ontario, Canada, N2L 3C5
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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.
Keywords: Kepler problem on the sphere, Ligon-Shaaf regularization, geodesic flow on the sphere Kepler problem on the sphere, Ligon-Shaaf regularization, geodesic flow on the sphere
MSC Classifications: 70Fxx show english descriptions Dynamics of a system of particles, including celestial mechanics 70Fxx - Dynamics of a system of particles, including celestial mechanics
 

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