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

• Klimeš, Martin ^[1] ; Rousseau Christiane ^[2]
  1. [1] University of Vienna

     University of Vienna

     Innere Stadt, Austria

     
  2. [2] University of Montreal

     University of Montreal

     Canadá

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 3, 2020
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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 C∞ case, where we show that only versality is possible.