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arXiv · 2601.19547

Fold of a bifurcation solution from the figure-eight choreography in the three body problem

Hiroshi Fukuda·Hiroshi Ozaki
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Abstract

In the figure-eight choreography in the classical three-body problem, both-side bifurcation solutions sometimes fold on one side of the bifurcation point with cusp of action. Three numerical examples of a such fold for figure-eight choreography under the Lennard-Jones-type potential and one under the homogeneous potential are introduced. Up to the fourth order of representation variable of the Lyapunov-Schmidt reduced action in two dimensions with three-fold symmetry, the fold is analyzed. It is shown that the bifurcation solutions fold under a condition given by the third and fourth expansion coefficients.

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Hiroshi Fukuda, Hiroshi Ozaki. 2026-01-27. Fold of a bifurcation solution from the figure-eight choreography in the three body problem. https://arxiv.org/abs/2601.19547

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