Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bi-Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation
  variables   We discuss from a bi-Hamiltonian point of view the Hamilton-Jacobi
separability of a few dynamical systems. They are shown to admit, in their
natural phase space, a quasi-bi-Hamiltonian formulation of Pfaffian type. This
property allows us to straightforwardly recover a set of separation variables
for the corresponding Hamilton-Jacobi equation.

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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th