Regularization of the Kepler Problem on the Three-sphere

被引：2

作者：

Hu, Shengda ^{[1
]}

Santoprete, Manuele ^{[1
]}

机构：

[1] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2014年 / 66卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Kepler problem on the sphere; Ligon-Shaaf regularization; geodesic flow on the sphere; N-BODY PROBLEM; CONSTANT CURVATURE; SPACES; GEOMETRY; VECTOR;

D O I：

10.4153/CJM-2012-039-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：760 / 782

页数：23

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