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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Polygonal homographic orbits in spaces of constant curvature


Author: Pieter Tibboel
Journal: Proc. Amer. Math. Soc. 141 (2013), 1465-1471
MSC (2010): Primary 00A69, 37N05, 70F10, 70F15
Published electronically: August 23, 2012
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the geometry of the 2-dimensional $ n$-body problem for spaces of constant curvature $ \kappa \neq 0$, $ n\geq 3$, does not allow for polygonal homographic solutions, provided that the corresponding orbits are irregular polygons of non-constant size.


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Additional Information

Pieter Tibboel
Affiliation: Department of Mathematics & Statistics, Chongqing University, Chongqing, 400044, People’s Republic of China
Address at time of publication: Department of Mathematics, Y6524 (Yellow Zone) 6/F Academic 1, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong
Email: Pieter.Tibboel@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11410-8
PII: S 0002-9939(2012)11410-8
Received by editor(s): August 11, 2011
Published electronically: August 23, 2012
Communicated by: Walter Craig
Article copyright: © Copyright 2012 American Mathematical Society