Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Hamiltonian structures for Ermakov systems   We construct Poisson structures for Ermakov systems, using the Ermakov
invariant as the Hamiltonian. Two classes of Poisson structures are obtained,
one of them degenerate, in which case we derive the Casimir functions. In some
situations, the existence of Casimir functions can give rise to superintegrable
Ermakov systems. Finally, we characterize the cases where linearization of the
equations of motion is possible.

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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph