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Poisson Brackets with Prescribed Casimirs

Published online by Cambridge University Press:  20 November 2018

Pantelis A. Damianou
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus email: damianou@ucy.ac.cypetalido@ucy.ac.cy
Fani Petalidou
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus email: damianou@ucy.ac.cypetalido@ucy.ac.cy
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Abstract

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We consider the problem of constructing Poisson brackets on smooth manifolds $M$ with prescribed Casimir functions. If $M$ is of even dimension, we achieve our construction by considering a suitable almost symplectic structure on $M$, while, in the case where $M$ is of odd dimension, our objective is achieved using a convenient almost cosymplectic structure. Several examples and applications are presented.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2012

References

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