Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Meromorphically integrable homogeneous potentials with multiple Darboux
  points   We prove that the only meromorphically integrable planar homogeneous
potential of degree k <> -2,0,2 having a multiple Darboux point is the
potential invariant by rotation. This case is a singular case of the
Maciejewski-Przybylska relation on eigenvalues at Darboux points of homogeneous
potentials, and needed before a case by case special analysis. The most
striking application of this Theorem is the complete classification of
integrable real analytic homogeneous potentials in the plane of negative
degree.

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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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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: solv-int
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The categories of this paper are: gr-qc