Critical points at infinity in charged N-body systems

TL;DR

This paper introduces the concept of critical points at infinity in charged N-body systems, characterizes them, and explores their role in bifurcations, with specific analysis for the charged 3-body problem.

Contribution

It extends the notion of critical points at infinity to charged N-body systems and provides a characterization and analysis framework, including bifurcation values.

Findings

Critical points at infinity are characterized for charged N-body systems.

They are essential for understanding bifurcations of the integral map.

Bifurcation values are identified for the charged 3-body problem.

Abstract

We define the notion of critical points at infinity for the charged N-body problem, following the approach of Albouy 1993. We give a characterisation of such points and show how they can be found in the charged 3-body problem. The symmetry group of the N-body problem and accompanying integrals play a key role. In fact critical points at infinity are indispensible in understanding the bifurcations of the integral map. Together with the critical points at infinity in the charged 3-body problem, we present the bifurcation values.