# American Institute of Mathematical Sciences

March  2014, 34(3): 1229-1249. doi: 10.3934/dcds.2014.34.1229

## Generating functions and volume preserving mappings

 1 Department of Mathematics, University of Bergen, P.O. Box 7800, N-5020 Bergen, Norway, Norway

Received  November 2012 Revised  February 2013 Published  August 2013

In this paper, we study generating forms and generating functions for volume preserving mappings in $\mathbf{R}^n$. We derive some parametric classes of volume preserving numerical schemes for divergence free vector fields. In passing, by extension of the Poincaré 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.
Citation: Huiyan Xue, Antonella Zanna. Generating functions and volume preserving mappings. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 1229-1249. doi: 10.3934/dcds.2014.34.1229
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