Lagrangian reduction of symmetric discrete mechanical systems: a survey

In this note we survey some of our results on the Lagrangian reduction of discrete-time mechanical systems (DMSs). It is intended as an introduction to the general ideas that we used in the reduction of DMSs with nonholonomic constraints, DMSs with external forcing, as well as a theory of reduction by stages for such systems. This line of work was inspired by the paper and the monograph written by H. Cendra, J. Marsden and T. Ratiu in 2001.