What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration (Q2758133)

In recent years the research on geometrical numerical integrators for differential equations (i.e. integrators which preserve some property of the flow of the differential equation) has been the subject of an increasing number of publications. Here the authors attempt to give a theoretical classification of these geometric integrators (and also more general dynamical systems) by using the associated groups of diffeomorphisms. NEWLINENEWLINENEWLINEIn addition this study permits to give a unified view of symplectic, Lie group and other geometric integrators. For the interested reader it must be noticed that some basic results on Lie groups such as Cartan's classification of the infinite dimensional pseudogroups on a real manifold are outlined and a number of selected examples are included to make easier the understanding of the subject.