location:  Publications → journals → CJM
Abstract view

# 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
 Format: LaTeX MathJax PDF

## 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
 MSC Classifications: 70Fxx - Dynamics of a system of particles, including celestial mechanics

 top of page | contact us | privacy | site map |