Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of singularities in the problem of motion of the
  Kovalevskaya top in a double force field   The problem of motion of the Kovalevskaya top in a double force field is
investigated (the integrable case of A.G. Reyman and M.A. Semenov-Tian-Shansky
without a gyrostatic momentum). It is a completely integrable Hamiltonian
system with three degrees of freedom not reducible to a family of systems with
two degrees of freedom. The critical set of the integral map is studied. The
critical subsystems and bifurcation diagrams are described. The classification
of all nondegenerate critical points is given. The set of these points consists
of equilibria (nondegenerate singularities of rank 0), of singular periodic
motions (nondegenerate singularities of rank 1), and also of critical
two-frequency motions (nondegenerate singularities of rank 2).

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The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
2
The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: q-fin