Discrete dynamics in implicit form

Abstract

A notion of implicit difference equation on a Lie groupoid is introducedand an algorithm for extracting the integrable part (backward or/and forward) is formulated.As an application, we prove that discrete Lagrangiandynamics on a Lie groupoid $G$ may be described in terms of Lagrangian implicit differenceequations of the corresponding cotangent groupoid $T^*G$. Other situations include finitedifference methods for time-dependent linear differential-algebraic equations and discretenonholonomic Lagrangian systems, as parti-cular examples.