Uniqueness results for co-circular central configurations for power-law potentials
Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III)
Hall, Glen Richard (Boston University. Department of Mathematics and Statistics)
Roberts, Gareth E. (College of the Holy Cross. Dept. of Mathematics and Computer Science)

Date:	2014
Abstract:	For a class of potential functions including those used for the planar n-body and n-vortex problems, we investigate co-circular central configurations whose center of mass coincides with the center of the circle containing the bodies. Useful equations are derived that completely describe the problem. Using a topological approach, it is shown that for any choice of positive masses (or circulations), if such a central configuration exists, then it is unique. It quickly follows that if the masses are all equal, then the only solution is the regular n-gon. For the planar n-vortex problem and any choice of the vorticities, we show that the only possible cocircular central configuration with center of vorticity at the center of the circle is the regular n-gon with equal vorticities.
Note:	Agraïments: The authors would like to thank the two reviewers for their helpful comments concerning this work. GR was supported by a grant from the National Science Foundation (DMS-1211675).
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Central configuration ; N-body problem ; N-vortex problem ; Co-circular central configuration
Published in:	Physica D. Nonlinear phenomena, Vol. 280-281 (2014) , p. 44-47, ISSN 0167-2789

DOI: 10.1016/j.physd.2014.05.003

Postprint 9 p, 245.8 KB

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