Geodesic
Finiteness of central configurations of five bodies in the plane
Alain Albouy1 ; Vadim Kaloshin2
1 CNRS-UMR8028, Observatoire de Paris, 77, avenue Denfert-Rochereau, 75014 Paris, France
2 Department of Mathematics, University of Maryland, College Park, MD 20742-4015
Annals of mathematics, Tome 176 (2012) no. 1, pp. 535-588.

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We prove there are finitely many isometry classes of planar central configurations (also called relative equilibria) in the Newtonian 5-body problem, except perhaps if the 5-tuple of positive masses belongs to a given codimension 2 subvariety of the mass space.
DOI : 10.4007/annals.2012.176.1.10

Alain Albouy 1 ; Vadim Kaloshin 2

1 CNRS-UMR8028, Observatoire de Paris, 77, avenue Denfert-Rochereau, 75014 Paris, France
2 Department of Mathematics, University of Maryland, College Park, MD 20742-4015 
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Alain Albouy; Vadim Kaloshin. Finiteness of central configurations of five bodies in the plane. Annals of mathematics, Tome 176 (2012) no. 1, pp. 535-588. doi : 10.4007/annals.2012.176.1.10. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.1.10/

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