Fold of a bifurcation solution from the figure-eight choreography in the three body problem
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909012953399296 |
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| author | Fukuda, Hiroshi Ozaki, Hiroshi |
| author_facet | Fukuda, Hiroshi Ozaki, Hiroshi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_19547 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fold of a bifurcation solution from the figure-eight choreography in the three body problem Fukuda, Hiroshi Ozaki, Hiroshi Mathematical Physics 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. |
| title | Fold of a bifurcation solution from the figure-eight choreography in the three body problem |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2601.19547 |