Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kovalevskaya exponents and the space of initial conditions of a
  quasi-homogeneous vector field   Formal series solutions and the Kovalevskaya exponents of a quasi-homogeneous
polynomial system of differential equations are studied by means of a weighted
projective space and dynamical systems theory. A necessary and sufficient
condition for the series solution to be a convergent Laurent series is given,
which improve the well known Painlev\'{e} test. In particular, if a given
system has the Painlev\'{e} property, an algorithm to construct Okamoto's space
of initial conditions is given. The space of initial conditions is obtained by
weighted blow-ups of the weighted projective space, where the weights for the
blow-ups are determined by the Kovalevskaya exponents. The results are applied
to the first Painlev\'{e} hierarchy ($2m$-th order first Painlev\'{e}
equation).

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The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph