Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lax Pairs for Linear Hamiltonian Systems   In the paper Lax pairs for linear Hamiltonian systems of differential
equations are constructed. In particular, Gr\"obner bases are used for the
computations. It is proved that the maps which appear in the construction of
Lax pairs are Poisson. Various properties of first integrals of the system
which are obtained from the Lax pairs are investigated.

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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph