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arXiv · 1103.0849

Poisson brackets with prescribed Casimirs

Pantelis A. Damianou·Fani Petalidou
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Abstract

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 by using a convenient almost cosymplectic structure. Several examples and applications are presented.

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Pantelis A. Damianou, Fani Petalidou. 2011-03-04. Poisson brackets with prescribed Casimirs. https://doi.org/10.4153/cjm-2011-082-2

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