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Discrete dynamics in implicit form

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  • A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie groupoid $G$ may be described in terms of Lagrangian implicit difference equations of the corresponding cotangent groupoid $T^*G$. Other situations include finite difference methods for time-dependent linear differential-algebraic equations and discrete nonholonomic Lagrangian systems, as parti-cular examples.
    Mathematics Subject Classification: Primary: 34K32, 22A22; Secondary: 17B66, 37M15, 57D17.


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