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arXiv · 0812.3333

On the singularities of the curved n-body problem

Florin Diacu
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Abstract

We study singularities of the n-body problem in spaces of constant curvature and generalize certain results due to Painleve, Weierstrass, and Sundman. For positive curvature, some of our proofs use the correspondence between total collision solutions of the original system and their orthogonal projection--a property that offers a new method of approaching the problem in this particular case.

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Florin Diacu. 2009-11-10. On the singularities of the curved n-body problem. https://arxiv.org/abs/0812.3333

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