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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generic finiteness for Dziobek configurations


Author: Richard Moeckel
Journal: Trans. Amer. Math. Soc. 353 (2001), 4673-4686
MSC (1991): Primary 70F10, 70F15, 37N05
Published electronically: April 24, 2001
MathSciNet review: 1851188
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Abstract | References | Similar Articles | Additional Information

Abstract: The goal of this paper is to show that for almost all choices of $n$ masses, $m_i$, there are only finitely many central configurations of the Newtonian $n$-body problem for which the bodies span a space of dimension $n-2$ (such a central configuration is called a Dziobek configuration). The result applies in particular to two-dimensional configurations of four bodies and three-dimensional configurations of five bodies.


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Additional Information

Richard Moeckel
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: rick@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02828-8
PII: S 0002-9947(01)02828-8
Keywords: Celestial mechanics, central configurations, $n$-body problem
Received by editor(s): December 29, 2000
Published electronically: April 24, 2001
Article copyright: © Copyright 2001 American Mathematical Society