Martin Klimeš

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20172021

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math.DS2020

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

Martin Klimes, Christiane Rousseau

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-contai…

math.DS2019

Remarks on rational vector fields on $C P^{1}$

Martin Klimeš, Christiane Rousseau

In this paper we introduce geometric tools to study the families of rational vector fields of a given degree over $C P^{1}$ . To a generic vector field of such a parame…

math.DS2017

Generic 2-parameter perturbations of parabolic singular points of vector fields in C

Martin Klimes, Christiane Rousseau

We describe the equivalence classes of germs of generic $2$ -parameter families of complex vector fields $z ˙ = ω_{ε} (z)$ on $C$ unfolding a singular parabolic point of mu…

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

Remarks on rational vector fields on CP1

Generic 2-parameter perturbations of parabolic singular points of vector fields in C

Remarks on rational vector fields on $C P^{1}$