从多边形到超离散潘勒韦方程
From Polygons to Ultradiscrete Painlevé Equations
摘要：
热带亏格1曲线的射线以定义有界多边形的方式受到约束。当我们放松这个约束时，生成的曲线不会闭合，从而产生螺旋多边形系统。分段线性变换保持这些射线的形式，形成仿射外尔型群的热带有理表示。我们提出了一个选择的螺旋多边形与3至11边的分段线性变换组符合Bäcklund变换和超离散潘勒韦方程的发展方程。
英文摘要：
The rays of tropical genus one curves are constrained in a way that defines a bounded polygon. When we relax this constraint, the resulting curves do not close, giving rise to a system of spiraling polygons. The piecewise linear transformations that preserve the forms of those rays form tropical rational presentations of groups of affine Weyl type. We present a selection of spiraling polygons with three to eleven sides whose groups of piecewise linear transformations coincide with the Bäcklund transformations and the evolution equations for the ultradiscrete Painlevé equations.
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