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arXiv:0812.3333 [math.DS]AbstractReferencesReviewsResources

On the singularities of the curved n-body problem

Florin Diacu

Published 2008-12-17, updated 2009-11-10Version 3

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.

Comments: 20 pages
Journal: Trans. Amer. Math. Soc. 363 (4), (2011), 2249-2264
Categories: math.DS, math-ph, math.MP
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