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On Centered Co-circular Central Configurations of the n-Body Problem

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Abstract

We study the co-circular central configurations of the n-body problem for which the center of mass and the center of the common circle coincide. In particular, we prove that there are no central configurations of this type with all the masses equal except one. This provides more evidences for the veracity of the conjecture that the regular n-gon with equal masses is the unique co-circular central configuration of the n-body problem whose center of mass is the center of the circle. Our result remains valid if we consider power-law potentials.

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Authors and Affiliations

  1. Facultat de Ciències i Tecnologia, Universitat de Vic - Universitat Central de Catalunya (UVic-UCC), 08500, Vic, Spain

    Montserrat Corbera

  2. Departamento de Matemàtica, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisbon, Portugal

    Claudia Valls

Authors
  1. Montserrat Corbera
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  2. Claudia Valls
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Correspondence to Montserrat Corbera.

Additional information

Montserrat Corbera is supported by the MINECO-FEDER Grant MTM2016-77278-P. Claudia Valls is supported by FCT/Portugal through UID/MAT/04459/2013.

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Corbera, M., Valls, C. On Centered Co-circular Central Configurations of the n-Body Problem. J Dyn Diff Equat 31, 2053–2060 (2019). https://doi.org/10.1007/s10884-018-9699-2

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  • DOI: https://doi.org/10.1007/s10884-018-9699-2

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