Abstract:Generally, the term “discretization” refers to a procedure that turns a differential equation into difference equations involving only finitely many variables, whose solutions approximate those of the differential equation. In differential geometry, structure-preserving discretization is the essence of discrete differential geometry. In dynamics, geometric integration is the subfield that is concerned with structure-preserving discretization. The common idea behind these developments in geometry and dynamics is to find and investigate discrete models that exhibit properties and structures characteristic of the corresponding smooth geometric objects and dynamical processes. The resulting discretization constitutes a mathematical theory, which incorporates the classical analog in the continuous limit. In the talk some concrete examples of structure preserving discretizations as well as their applications will be presented.