On the universal unfolding of vector fields in one variable: A proof of Kostov's theorem

Autor:	Klimes, Martin, Rousseau, Christiane
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems Mathematics - Classical Analysis and ODEs 37F75 32M25 32S65 34M99
Druh dokumentu:	Working Paper
Popis:	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 $C^\infty$ case, where we show that only versality is possible. Comment: 11 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2002.08444 Zobrazit plný text záznamu View this record from Arxiv