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

Generating forms for exact volume-preserving maps

H. E. Lomelí 1, and  J. D. Meiss 2,

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 $\R^n$.
Keywords: incompressible, differential forms., symplectic, volume preserving.
Mathematics Subject Classification: 37J45, 53D22, 70H15, 37J1.
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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