# American Institute of Mathematical Sciences

March  2013, 33(3): 1117-1135. doi: 10.3934/dcds.2013.33.1117

## Discrete dynamics in implicit form

 1 Unidad asociada ULL-CSIC “Geometría Diferencial y Mecánica Geométrica”, Departamento de Matemática Fundamental, Facultad de Matemáticas, Universidad de la Laguna, La Laguna, Tenerife, Canary Islands, Spain 2 Unidad asociada ULL-CSIC Geometría Diferencial y Mecánica Geométrica, Departamento de Matemática Fundamental, Facultad de Matemáticas, Universidad de la Laguna, La Laguna, Tenerife, Canary Islands, Spain 3 Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Campus de Cantoblanco, UAM, C/Nicolás Cabrera, 15, 28049 Madrid, Spain

Received  April 2011 Revised  November 2011 Published  October 2012

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.
Citation: David Iglesias-Ponte, Juan Carlos Marrero, David Martín de Diego, Edith Padrón. Discrete dynamics in implicit form. Discrete & Continuous Dynamical Systems - A, 2013, 33 (3) : 1117-1135. doi: 10.3934/dcds.2013.33.1117
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