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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The number of planar central configurations is finite when $N-1$ mass positions are fixed
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by Peter W. Lindstrom PDF
Trans. Amer. Math. Soc. 353 (2001), 291-311 Request permission

Abstract:

In this paper, it is proved that for $n>2$ and $n\not =4$, if $n-1$ masses are located at fixed points in a plane, then there are only a finite number of $n$-point central configurations that can be generated by positioning a given additional $n$th mass in the same plane. The result is established by proving an equivalent isolation result for planar central configurations of five or more points. Other general properties of central configurations are established in the process. These relate to the amount of centrality lost when a point mass is perturbed and to derivatives associated with central configurations.
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Additional Information
  • Peter W. Lindstrom
  • Affiliation: Department of Mathematics, Saint Anselm College, Manchester, New Hampshire 03102
  • Received by editor(s): December 18, 1998
  • Published electronically: September 18, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 291-311
  • MSC (2000): Primary 70F10
  • DOI: https://doi.org/10.1090/S0002-9947-00-02568-X
  • MathSciNet review: 1695029