Abelian integrals arise in the mathematical description of various physical processes. According to Abel's theorem these integrals are related to motion of a set of points along a plane curve around fixed points, which are relatively little used in physics applications. We propose to interpret coordinates of the fixed points either as parameters of exact discretization or as additional first integrals for equations of motion reduced to Abelian quadratures.

中文翻译：

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离散化和超可积性合二为一

阿贝尔积分出现在各种物理过程的数学描述中。根据阿贝尔定理，这些积分与一组点围绕固定点沿平面曲线的运动有关，这些点在物理应用中的使用相对较少。我们建议将固定点的坐标解释为精确离散化的参数或作为减少到阿贝尔求积的运动方程的附加第一积分。