Lissajous 3-braids

Eiko Kin; Hiroaki Nakamura; Hiroyuki Ogawa

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arXiv · 2008.00585

Lissajous 3-braids

Eiko Kin·Hiroaki Nakamura·Hiroyuki Ogawa

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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.

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Eiko Kin, Hiroaki Nakamura, Hiroyuki Ogawa. 2020-08-02. Lissajous 3-braids. https://arxiv.org/abs/2008.00585

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