Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic 1-parameter pertubations of a vector field with a singular point
  of codimension k   We describe the equivalence classes of germs of generic 1-parameter families
of complex vector fields z dot = omega_epsilon(z) on C unfolding a singular
point of multiplicity k+1: omega_0 = z^{k+1} + o(z^{k+1}). The equivalence is
under conjugacy by holomorphic change of coordinate and parameter. We provide a
description of the modulus space and (almost) unique normal forms. As a
preparatory step, we present the complete bifurcation diagram of the family of
vector fields z dot = z^{k+1} - epsilon, over CP1.

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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph