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Matched pairs of discrete dynamical systems
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Matched pairs of discrete dynamical systems
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Matched pairs of Lie groupoids and Lie algebroids are studied. Discrete Euler-Lagrange equations are written for the matched pairs of Lie groupoids. As such, a geometric framework to analyse a discrete system by decomposing it into two mutually interacting subsystems is established. Two examples are provided to illustrate this strategy; the discrete dynamics on the trivial groupoid, and the discrete dynamics on the special linear group.
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