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

Martin Klimes; Christiane Rousseau

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arXiv · 2002.08444

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

Martin Klimes·Christiane Rousseau

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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 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.

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Martin Klimes, Christiane Rousseau. 2020-02-19. On the universal unfolding of vector fields in one variable: A proof of Kostov's theorem. https://arxiv.org/abs/2002.08444

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