12 citations · 12 across the 6 of their papers we have counts for
10 papers
Reading analytic invariants of parabolic diffeomorphisms from their orbits
Martin Klimes, Pavao Mardesic, Goran Radunovic +1
In this paper we study germs of diffeomorphisms in the complex plane. We address the following problem: How to read a diffeomorphism knowing one of its orbits ? We…
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 admitting a formal first integral but no holomorphic first integral. These examples are related to a question raised by…
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 -dimensional vector field. First we provide a self-contai…
Remarks on rational vector fields on
Martin Klimeš, Christiane Rousseau
In this paper we introduce geometric tools to study the families of rational vector fields of a given degree over . To a generic vector field of such a parame…
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…
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 -parameter families of complex vector fields on unfolding a singular parabolic point of mu…
Stokes phenomenon and confluence in non-autonomous Hamiltonian systems
Martin Klimes
This article studies a confluence of a pair of regular singular points to an irregular one in a generic family of time-dependent Hamiltonian systems in dimension 2. This is a gener…
The wild monodromy of the Fifth Painlevé equation and its action on wild character variety: an approach of confluence
Martin Klimes
The article studies the Fifth Painlevé equation and of the nonlinear Stokes phenomenon at its irregular singularity at infinity from the point of view of confluence from the Sixth…
Confluence of singularities in hypergeometric systems
Martin Klimes
A system in a Birkhoff normal form with an irregular singularity of Poincare rank 1 at the origin and a regular singularity at infinity is through the Borel-Laplace transform dual…
Confluence of singularities of non-linear differential equations via Borel--Laplace transformations
Martin Klimes
Borel summable divergent series usually appear when studying solutions of analytic ODE near a multiple singular point. Their sum, uniquely defined in certain sectors of the complex…