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Spatial Double Choreographies of the Newtonian 2n-Body Problem

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Abstract

In this paper, for the spatial Newtonian 2n-body problem with equal masses, by proving that the minimizers of the action functional under certain symmetric, topological and monotone constraints are collision-free, we found a family of spatial double choreographies, which have the common feature that half of the masses are circling around the z-axis clockwise along a spatial loop, while the motions of the other half of the masses are given by a rotation of the first half around the x-axis by π. Both loops are simple, without any self-intersection, and symmetric with respect to the xz-plane and yz-plane. The set of intersection points between the two loops is non-empty and contained in the xy-plane. The number of such double choreographies grows exponentially as n goes to infinity.

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  1. Guowei Yu

    Present address: Dipartimento di Matematica “Giuseppe Peano”, Università degli Studi di Torino, Turin, Italy

Authors and Affiliations

  1. University of Paris-Dauphine & IMCCE, Paris Observatory, Paris, France

    Guowei Yu

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  1. Guowei Yu
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Correspondence to Guowei Yu.

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Communicated by P. Rabinowitz

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Yu, G. Spatial Double Choreographies of the Newtonian 2n-Body Problem. Arch Rational Mech Anal 229, 187–229 (2018). https://doi.org/10.1007/s00205-018-1216-6

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  • DOI: https://doi.org/10.1007/s00205-018-1216-6

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