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Generic finiteness for Dziobek configurations
Author(s):
Richard
Moeckel
Journal:
Trans. Amer. Math. Soc.
353
(2001),
4673-4686.
MSC (1991):
Primary 70F10, 70F15, 37N05
Posted:
April 24, 2001
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Abstract:
The goal of this paper is to show that for almost all choices of  masses,  , there are only finitely many central configurations of the Newtonian  -body problem for which the bodies span a space of dimension  (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:
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
Posted:
April 24, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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