On the singularities of the curved $n$-body problem
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- by Florin Diacu PDF
- Trans. Amer. Math. Soc. 363 (2011), 2249-2264
Abstract:
We study singularities of the $n$-body problem in spaces of constant curvature and generalize certain results due to PainlevĂ©, Weierstrass, and Sundman. For positive curvature, some of our proofs use the correspondence between total collision solutions of the original system and their orthogonal projectionâa property that offers a new method of approaching the problem in this particular case.References
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Additional Information
- 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
- Email: diacu@math.uvic.ca
- Received by editor(s): July 22, 2009
- Received by editor(s) in revised form: November 10, 2009
- Published electronically: October 1, 2010
- © Copyright 2010 by Florin Diacu
- Journal: Trans. Amer. Math. Soc. 363 (2011), 2249-2264
- MSC (2010): Primary 70F15
- DOI: https://doi.org/10.1090/S0002-9947-2010-05251-1
- MathSciNet review: 2746682