Discrete Euler–Lagrange equations are studied over double cross product Lie groupoids. As such, a geometric framework for the local analysis of a discrete dynamical system is established. The arguments are elucidated on the local discrete dynamics of a gauge groupoid. The discrete Elroy’s beanie is studied as a physical example.

中文翻译：

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双叉积李群上的离散动力系统

在双叉积李群上研究离散欧拉-拉格朗日方程。因此，建立了离散动力系统局部分析的几何框架。这些论点是在规范群的局部离散动力学上阐明的。离散的 Elroy 无檐小便帽作为物理示例进行了研究。