Generating forms for exact volume-preserving maps

H. E. Lomelí; J. D. Meiss

doi:10.3934/dcdss.2009.2.361

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2009, Volume 2, Issue 2: 361-377. Doi: 10.3934/dcdss.2009.2.361

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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
2.
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526

Received: February 29, 2008

Revised: May 31, 2008

Published: May 2009

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Abstract

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 $\R^n$.

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Mathematics Subject Classification: 37J45, 53D22, 70H15, 37J10.

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