On the Regularization of the Kepler Problem

TL;DR

This paper clarifies the geometric relationship between two regularization methods for the Kepler problem, revealing how the Ligon-Schaaf regularization can be viewed as an adaptation of Moser regularization, thus explaining the problem's hidden symmetry.

Contribution

It provides a geometric interpretation linking Ligon-Schaaf and Moser regularizations for the Kepler problem, enhancing understanding of their relationship.

Findings

Ligon-Schaaf regularization is an adaptation of Moser regularization

The geometric approach explains the hidden symmetry in the Kepler problem

Clarifies the connection between different regularization techniques

Abstract

We show that for the Kepler problem the canonical Ligon-Schaaf regularization map can be understood in a straightforward manner as an adaptation of the Moser regularization. In turn this explains the hidden symmetry in a geometric way.