Martin Klimeš

activity

20172021

collaborators

6 papers

math.CA2021

A remark on first integrals of vector fields

André Belotto da Silva, Martin Klimes, Julio C. Rebelo +1

We provide examples of vector fields on $(C^{3}, 0)$ admitting a formal first integral but no holomorphic first integral. These examples are related to a question raised by…

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.CA2019

On equivalence of singularities of linear second order ordinary differential equations by point transformations

Martin Klimes

The article provides a local classification of singularities of meromorphic second order linear differential equation with respect to analytic/meromorphic linear point transformati…

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…

math.CA2017

Stokes phenomenon and confluence in non-autonomous Hamiltonian systems