Abstract
We classify 3-braids arising from collision-free choreographic motions of 3 bodies on Lissajous plane curves, and present a parametrization in terms of levels and (Christoffel) slopes. Each of these Lissajous 3-braids represents a pseudo-Anosov mapping class whose dilatation increases when the level ascends in the natural numbers or when the slope descends in the Stern–Brocot tree. We also discuss 4-symbol frieze patterns that encode cutting sequences of geodesics along the Farey tessellation in relation to odd continued fractions of quadratic surds for the Lissajous 3-braids.
Funding Statement
This work was supported by JSPS KAKENHI Grant Numbers JP18K03299, JP21K03247, JP20H00115.
Citation
Eiko KIN. Hiroaki NAKAMURA. Hiroyuki OGAWA. "Lissajous 3-braids." J. Math. Soc. Japan 75 (1) 195 - 228, January, 2023. https://doi.org/10.2969/jmsj/86658665
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