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Spatial Convex but Non-strictly Convex Double-Pyramidal Central Configurations of the \((2n+2)\)-Body Problem

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Abstract

A configuration of the N bodies is convex if the convex hull of the positions of all the bodies in \(\mathbb {R}^3\) does not contain in its interior any of these bodies. And a configuration is strictly convex if the convex hull of every subset of the N bodies is convex. Recently some authors have proved the existence of convex but non-strictly convex central configurations for some N-body problems. In this paper we prove the existence of a new family of spatial convex but non-strictly convex central configurations of the \((2n+2)\)-body problem.

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Acknowledgements

Both authors are partially supported by the Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación Grants MTM2016-77278-P (FEDER). The second author is also partially supported by the Agència de Gestió d’Ajuts Universitaris i de Recerca Grant 2017SGR1617, and the H2020 European Research Council Grant MSCA-RISE-2017-777911.

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Authors and Affiliations

  1. Departament d’Enginyeries, Universitat de Vic–Universitat Central de Catalunya, C/ Laura 13, 08500, Vic, Barcelona, Spain

    Montserrat Corbera

  2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain

    Jaume Llibre

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  1. Montserrat Corbera
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  2. Jaume Llibre
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Correspondence to Montserrat Corbera.

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Corbera, M., Llibre, J. Spatial Convex but Non-strictly Convex Double-Pyramidal Central Configurations of the \((2n+2)\)-Body Problem. J Dyn Diff Equat 32, 1965–1982 (2020). https://doi.org/10.1007/s10884-019-09798-3

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  • DOI: https://doi.org/10.1007/s10884-019-09798-3

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