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On the Uniqueness of Co-circular Four Body Central Configurations

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Abstract

We study central configurations lying on a common circle in the Newtonian four-body problem. Using a topological argument we prove that there is at most one co-circular central configuration for each cyclic ordering of the masses on the circle.

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Acknowledgements

I would like to thank Alain Albouy, Shengda Hu, Steven Karp, Santiago López de Medrano, and Alessandro Portaluri for interesting discussions on this work. This work was supported by an NSERC discovery grant.

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Authors and Affiliations

  1. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Manuele Santoprete

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  1. Manuele Santoprete
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Correspondence to Manuele Santoprete.

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Communicated by P. Rabinowitz.

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Santoprete, M. On the Uniqueness of Co-circular Four Body Central Configurations. Arch Rational Mech Anal 240, 971–985 (2021). https://doi.org/10.1007/s00205-021-01626-7

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