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arXiv · 2112.07267

Critical points at infinity in charged N-body systems

I. Hoveijn·H. Waalkens·M. Zaman
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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.

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I. Hoveijn, H. Waalkens, M. Zaman. 2021-12-14. Critical points at infinity in charged N-body systems. https://arxiv.org/abs/2112.07267

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