On the Universal Unfolding of Vector Fields in One Variable: A Proof of Kostov’s Theorem

@article{Klime2020OnTU,
  title={On the Universal Unfolding of Vector Fields in One Variable: A Proof of Kostov’s Theorem},
  author={Martin Klime{\vs} and Christiane Rousseau},
  journal={Qualitative Theory of Dynamical Systems},
  year={2020}
}
In this note we present variants of Kostov’s theorem on a versal deformation of a parabolic point of a complex analytic 1-dimensional vector field. First we provide a self-contained proof of Kostov’s theorem, together with a proof that this versal deformation is indeed universal. We then generalize to the real analytic and formal cases, where we show universality, and to the $${\mathcal {C}}^\infty $$ C ∞ case, where we show that only versality is possible. 
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