Discrete dynamical systems over double cross-product Lie groupoids

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.

Automated summary

The study establishes a geometric framework for the local analysis of discrete dynamical systems on double cross product Lie groupoids, with a focus on discrete Euler-Lagrange equations. The arguments elucidate the local discrete dynamics of a gauge groupoid and study the discrete Elroy's beanie as a physical example.