Critical points at infinity in charged [formula omitted]-body systems

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.