Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Canonical transformations of the extended phase space, Toda lattices and
  Stackel family of integrable systems   We consider compositions of the transformations of the time variable and
canonical transformations of the other coordinates, which map completely
integrable system into other completely integrable system. Change of the time
gives rise to transformations of the integrals of motion and the Lax pairs,
transformations of the corresponding spectral curves and R-matrices. As an
example, we consider canonical transformations of the extended phase space for
the Toda lattices and the Stackel systems.

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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex