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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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New equations for central configurations and generic finiteness
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by Thiago Dias PDF
Proc. Amer. Math. Soc. 145 (2017), 3069-3084 Request permission

Abstract:

We consider the finiteness problem for central configurations of the $n$-body problem. We prove that, for $n\geq 4$, there exists a (Zariski) closed subset $B$ in the mass space $\mathbb {R}^{n}$, such that if $(m_1,\dots ,m_n) \in \mathbb {R}^n\setminus B$, then there is a finite number of corresponding classes of $(n-2)$-dimensional central configurations for potential associated to a semi-integer exponent. Also, we obtain trilinear homogeneous polynomial equations of degree $3$ for central configurations of fixed dimension and, for each integer $k \geq 1$, we show that the set of mutual distances associated to a $k$-dimensional central configuration is contained in a determinantal algebraic set.
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Additional Information
  • Thiago Dias
  • Affiliation: Departamento de Matemática, Universidade Federal Rural de Pernambuco - Rua Dom Manuel de Medeiros s/n, 52171-900, Recife, Pernambuco, Brasil
  • Email: thiago.diasoliveira@ufrpe.br
  • Received by editor(s): January 22, 2016
  • Received by editor(s) in revised form: June 18, 2016, and August 8, 2016
  • Published electronically: January 6, 2017
  • Communicated by: Yingfei Yi
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 3069-3084
  • MSC (2010): Primary 70F10, 70F15, 37N05, 14A10
  • DOI: https://doi.org/10.1090/proc/13427
  • MathSciNet review: 3637954