# American Institute of Mathematical Sciences

June  2009, 2(2): 361-377. doi: 10.3934/dcdss.2009.2.361

## Generating forms for exact volume-preserving maps

 1 Department of Mathematics, Instituto Tecnológico Autónomo de México, Mexico 2 Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526, United States

Received  March 2008 Revised  June 2008 Published  April 2009

We develop a general theory of implicit generating forms for volume-preserving diffeomorphisms on a manifold. Our results generalize the classical formulas for generating functions of symplectic twist maps and examples of Carroll for volume-preserving maps on $\R^n$.
Citation: H. E. Lomelí, J. D. Meiss. Generating forms for exact volume-preserving maps. Discrete and Continuous Dynamical Systems - S, 2009, 2 (2) : 361-377. doi: 10.3934/dcdss.2009.2.361
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