Generating function and volume preserving mappings

Abstract

In this paper, we study generating forms and generating functions for volume preserving mappings in Rn. We derive some parametric classes of volume preserving numerical schemes for divergence free vector fields. In passing, by extension of the Poincar´e generating function and a change of variables, we obtained symplectic equivalent of the theta-method for differential equations, which includes the implicit midpoint rule and symplectic Euler A and B methods as special cases.