Fold of a bifurcation solution from the figure-eight choreography in the three body problem
Mathematical Physics
2026-05-06 v2 math.MP
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.
Cite
@article{arxiv.2601.19547,
title = {Fold of a bifurcation solution from the figure-eight choreography in the three body problem},
author = {Hiroshi Fukuda and Hiroshi Ozaki},
journal= {arXiv preprint arXiv:2601.19547},
year = {2026}
}