Generating functions and volume preserving mappings

Huiyan Xue; Antonella Zanna

doi:10.3934/dcds.2014.34.1229

Article Contents

2014, Volume 34, Issue 3: 1229-1249. Doi: 10.3934/dcds.2014.34.1229

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Generating functions and volume preserving mappings

Huiyan Xue^1, and
Antonella Zanna^1,

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

Received: November 2012

Revised: February 2013

Published: March 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 53D22, 70H15; Secondary: 65L05.

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