Classification of rational functions in symplectic and metric spaces

We consider symplectic and orthogonal classifications of rational functions of many variables. The main idea of these classifications consists in the use of methods of the differential geometry and the geometric theory of jet spaces. Namely, we consider group actions on an infinite jet space (rather than on functions), which allows us to find fields of differential invariants of these groups. Finally, we prove that dependencies between basic differential invariants and their derivatives completely determine the orbit of the corresponding function.