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# Poisson brackets with prescribed Casimirs

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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.

### Most cited references12

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### The local structure of Poisson manifolds

(1983)
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### The Toda lattice. II. Existence of integrals

(1974)
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### Les variétés de Poisson et leurs algèbres de Lie associées

(1977)
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### Author and article information

###### Journal
04 March 2011
1103.0849