Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincare' and Lie renormalized forms for regular singular points of
  vector fields in the plane   We discuss the local behaviour of vector fields in the plane $\R^2$ around a
regular singular point, using recently introduced reduced normal forms, i.e.
Poincar\'e and Lie renormalized forms [{\it Lett. Math. Phys.} {\bf 42} (1997),
103-114; {\it Ann. Inst. H. Poincar\'e (Phys. Theo.)} {\bf 70} (1999), 461-514;
{\it Lett. Math. Phys.} {\bf 57} (2001), 41-60]. We give a complete
classification, and provide explicit formulas, using Poincar\'e renormalized
forms for non-degenerate cases, and Lie ones for certain degenerate cases. Both
schemes are completely algorithmic, prove to be easy to implement, and only
require to solve linear equations.

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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol