Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the singularities of the curved $ n$-body problem

Author: Florin Diacu
Journal: Trans. Amer. Math. Soc. 363 (2011), 2249-2264
MSC (2010): Primary 70F15
Published electronically: October 1, 2010
MathSciNet review: 2746682
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Abstract: We study singularities of the $ n$-body problem in spaces of constant curvature and generalize certain results due to Painlevé, 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
Affiliation: Pacific Institute for the Mathematical Sciences, and Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, British Columbia, Canada V8W 3R4

Received by editor(s): July 22, 2009
Received by editor(s) in revised form: November 10, 2009
Published electronically: October 1, 2010
Article copyright: © Copyright 2010 by Florin Diacu