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Generating functions and volume preserving mappings

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


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