Schlicht Holomorphic Functions an the Riccati Differntial Equation.
Second order differential equations with complex-valued coefficients
Sectorial oscillation of linear differential equations and iterated order.
Selbstadjungierte Differentialoperatoren erster Ordnung in A2 (Co).
Semicompleteness of homogeneous quadratic vector fields
We investigate the quadratic homogeneous holomorphic vector fields on that are semicomplete, this is, those whose solutions are single-valued in their maximal definition domain. To a generic quadratic vector field we rationally associate some complex numbers that turn out to be integers in the semicomplete case, thus showing that the linear equivalence classes of semicomplete vector fields are contained in some sort of lattice in the space of linear equivalence classes of quadratic ones. We prove...
Semi-formal theory and Stokes' phenomenon of non-linear meromorphic systems of ordinary differential equations
This article continues earlier work of the author on non-linear systems of ordinary differential equations, published in Asymptotic Analysis 15 (1997), MR no. 98g:34015b. There, a completely formal theory was presented, while here we are concerned with a semi-formal approach: Solutions of non-linear systems of ordinary meromorphic differential equations are represented as, in general divergent, power series in several free parameters. The coefficients, aside from an exponential polynomial, a general...
Séries de -factorielles, opérateurs aux -différences et confluence
Singular sets of holonomy maps for algebraic foliations
In this article we investigate the natural domain of definition of a holonomy map associated to a singular holomorphic foliation of the complex projective plane. We prove that germs of holonomy between algebraic curves can have large sets of singularities for the analytic continuation. In the Riccati context we provide examples with natural boundary and maximal sets of singularities. In the generic case we provide examples having at least a Cantor set of singularities and even a nonempty open set...
Singularités des flots holomorphes
Nous mettons en évidence une obstruction au prolongement d’un germe de champ de vecteurs holomorphe en un champ holomorphe complet. En particulier, on démontre que toute singularité isolée d’un champ holomorphe complet sur une surface complexe possède un deuxième jet non nul.
Small divisors and large multipliers
We study germs of singular holomorphic vector fields at the origin of of which the linear part is -resonant and which have a polynomial normal form. The formal normalizing diffeomorphism is usually divergent at the origin but there exists holomorphic diffeomorphisms in some “sectorial domains” which transform these vector fields into their normal form. In this article, we study the interplay between the small divisors phenomenon and the Gevrey character of the sectorial normalizing diffeomorphisms....
Sobre La Cohomologia Asociada A Un Operador Lineal Diferencial Complejo.
Solution of the Schwarz differential equation.
Solutions entières d'un système d'équations aux différences. II
Soit un entier naturel non nul, et une fonction entière de variables complexes. Dans un article précédent, nous avons démontré dans le cas , que si est une solution d’un système de équations aux différences à coefficients polynomiaux dans deux directions différentes, avec une condition restrictive portant sur les équations, alors est le quotient d’un polynôme exponentiel par un polynôme. Dans cet article, nous démontrons ce résultat dans le cas général, et l’analogue pour le cas de...
Solutions of with prescribed sequences of zeros.
Solutions of that have almost all real zeros.
Solutions of non-homogeneous linear differential equations in the unit disc
The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation , where all coefficients , F ≢ 0 are analytic functions in the unit disc = z∈ℂ: |z|<1. We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.
Solutions of nonhomogeneous linear differential equations with exceptionally few zeros.
Solutions surstables des équations différentielles complexes lentes-rapides à point tournant
Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension.
Some addition to the generalized Riemann-Hilbert problem
We consider the generalized Riemann-Hilbert problem for linear differential equations with irregular singularities. If one weakens the conditions by allowing one of the Poincaré ranks to be non-minimal, the problem is known to have a solution. In this article we give a bound for the possibly non-minimal Poincaré rank. We also give a bound for the number of apparent singularities of a scalar equation with prescribed generalized monodromy data.