Regularization of the kepler problem on the three-sphere

Abstract

In this paper we regularize the Kepler problem on S3 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. © Canadian Mathematical Society 2012.