On a galoisian approach to the splitting of separatrices
On Certain Properties of Soloutions of Second-Order Linear Differential Equations.
On differential independence of the Riemann zeta function and the Euler gamma function
On differential rational invariants of finite subgroups of affine group.
On th order differential equations over Hardy fields
On rings of constants of derivations in two variables in positive characteristic
Let k be a field of chracteristic p > 0. We describe all derivations of the polynomial algebra k[x,y], homogeneous with respect to a given weight vector, in particular all monomial derivations, with the ring of constants of the form , where .
On Second Order Linear Differential Equations with Few Transcendental Solutions.
On the bialgebra of functional graphs and differential algebras.
On the calculation of some differential galois groups.
On the Galois theory of difference fields.
On the geometrization of a lemma of Singer and van der Put
In this paper, we give a geometrization and a generalization of a lemma of differential Galois theory, used by Singer and van der Put in their reference book. This geometrization, in addition of giving a nice insight on this result, offers us the opportunity to investigate several points of differential algebra and differential algebraic geometry. We study the class of simple Δ-schemes and prove that they all have a coarse space of leaves. Furthermore, instead of considering schemes endowed with...
On the problem of Baer and Kolchin in the Picard-Vessiot theory
We present the history of the development of Picard-Vessiot theory for linear ordinary differential equations. We are especially concerned with the condition of not adding new constants, pointed out by R. Baer. We comment on Kolchin's condition of algebraic closedness of the subfield of constants of the given differential field over which the equation is defined. Some new results concerning existence of a Picard-Vessiot extension for a homogeneous linear ordinary differential equation defined over...
On the structure of linear recurrent error-control codes
We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.
On the structure of linear recurrent error-control codes
We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.
Opérateurs hypergéométriques réductibles : décompositions et groupes de Galois différentiels
Opération de Cartier et vecteurs de Witt
Ordinary linear differential equations - a survey of the global theory
Overview of the differential Galois integrability conditions for non-homogeneous potentials
We report our recent results concerning integrability of Hamiltonian systems governed by Hamilton’s function of the form , where the potential V is a finite sum of homogeneous components. In this paper we show how to find, in the differential Galois framework, computable necessary conditions for the integrability of such systems. Our main result concerns potentials of the form , where and are homogeneous functions of integer degrees k and K > k, respectively. We present examples of integrable...