论文标题
lissajous 3编
Lissajous 3-braids
论文作者
论文摘要
我们对3个身体在lissajous平面曲线上的无碰撞编排动作产生的三架编分类，并以级别和（基督佛教）的斜率进行参数化。这些Lissajous 3编代代表一个伪-Anosov映射类别，当水平在自然数中上升或斜率下降时，其扩张会增加。我们还讨论了4个符号饰面模式，这些模式编码了沿Farey Tessellation的切割序列的切割序列，这些序列与lissajous 3架的二次SURDS的奇数持续分数有关。
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.
