Poisson brackets with prescribed Casimirs

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.

24 pages

References in corpus (1)

• Characterization, global analysis and integrability of a family of Poisson structures

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• Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems
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