Finiteness of central configurations of five bodies in the plane

Pages 535-588 from Volume 176 (2012), Issue 1 by Alain Albouy, Vadim Kaloshin

Abstract

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.

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      ZBLNUMBER = {1031.00005},
      }
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      AUTHOR = {Wintner, Aurel},
      TITLE = {The {A}nalytical {F}oundations of {C}elestial {M}echanics},
      SERIES = {Princeton Math. Ser.},
      VOLUME={5},
      PUBLISHER = {Princeton Univ. Press},
      ADDRESS = {Princeton, NJ},
      YEAR = {1941},
      PAGES = {xii+448},
      MRCLASS = {85.0X},
      MRNUMBER = {0005824},
      MRREVIEWER = {E. J. Moulton},
      ZBLNUMBER = {0026.02302},
      }
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    @article {Xia, MRKEY = {1106123},
      AUTHOR = {Xia, Zhihong},
      TITLE = {Central configurations with many small masses},
      JOURNAL = {J. Differential Equations},
      FJOURNAL = {Journal of Differential Equations},
      VOLUME = {91},
      YEAR = {1991},
      NUMBER = {1},
      PAGES = {168--179},
      ISSN = {0022-0396},
      CODEN = {JDEQAK},
      MRCLASS = {70F10 (70F15)},
      MRNUMBER = {1106123},
      MRREVIEWER = {Alexander Burov},
      DOI = {10.1016/0022-0396(91)90137-X},
      ZBLNUMBER = {0724.70015},
      }

Keywords
, , , ,
DOI
https://doi.org/10.4007/annals.2012.176.1.10
MR
2925390
zbMATH
06074021
Milestones
Received: 12 November 2010
Revised: 27 February 2011
Accepted: 3 June 2011
Published online: 1 July 2012

Authors

Alain Albouy

CNRS-UMR8028, Observatoire de Paris, 77, avenue Denfert-Rochereau, 75014 Paris, France

Vadim Kaloshin

Department of Mathematics, University of Maryland, College Park, MD 20742-4015