Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson brackets with prescribed Casimirs   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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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an