On the universal unfolding of vector fields in one variable: A proof of Kostov's theorem
Abstract
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 selfcontained 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 $C^\infty$ case, where we show that only versality is possible.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.08444
 Bibcode:
 2020arXiv200208444K
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Classical Analysis and ODEs;
 37F75;
 32M25;
 32S65;
 34M99
 EPrint:
 11 pages