Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completely Integrable Contact Hamiltonian Systems and Toric Contact
  Structures on $S^2\times S^3$   I begin by giving a general discussion of completely integrable Hamiltonian
systems in the setting of contact geometry. We then pass to the particular case
of toric contact structures on the manifold $S^2\times S^3$. In particular we
give a complete solution to the contact equivalence problem for a class of
toric contact structures, $Y^{p,q}$, discovered by physicists by showing that
$Y^{p,q}$ and $Y^{p',q'}$ are inequivalent as contact structures if and only if
$p\neq p'$.

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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: cs