Theoretical analysis demonstrates a hyperbolic reformulation of the figure-eight three-body choreography, highlighting geometric links to knot topology and lattice symmetries.
The figure‑eight three‑body choreography is reformulated using a complex shape parameter matching the hyperbolic structure of the figure‑eight knot complement. Its action becomes a hyperbolic geodesic functional, and the Eisenstein lattice’s unique fixed point serves as the FRLT pivot generating the orbit.
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Shin Tamaki (2026) studied this question.
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