Feuilletages de briot et Bouquet.
Feuilletages singuliers de codimension un, groupoïde de Galois et intégrales premières
Dans cet article, nous étudions le groupoïde de Galois d’un germe de feuilletage holomorphe de codimension un. Nous associons à ce -groupoïde de Lie un invariant biméromorphe : le rang transverse. Nous étudions en détails les relations entre cet invariant, l’existence de suites de Godbillon-Vey particulières et l’existence d’une intégrale première dans une extension fortement normale du corps différentiel des germes de fonctions méromorphes. Nous obtenons ainsi une généralisation d’un théorème...
Finite and infinite order of growth of solutions to linear differential equations near a singular point
In this paper, we investigate the growth of solutions of a certain class of linear differential equation where the coefficients are analytic functions in the closed complex plane except at a finite singular point. For that, we will use the value distribution theory of meromorphic functions developed by Rolf Nevanlinna with adapted definitions.
Finite order solutions of complex linear differential equations.
Finite-dimensional differential algebraic groups and the Picard-Vessiot theory
We make some observations relating the theory of finite-dimensional differential algebraic groups (the ∂₀-groups of [2]) to the Galois theory of linear differential equations. Given a differential field (K,∂), we exhibit a surjective functor from (absolutely) split (in the sense of Buium) ∂₀-groups G over K to Picard-Vessiot extensions L of K, such that G is K-split iff L = K. In fact we give a generalization to "K-good" ∂₀-groups. We also point out that the "Katz group" (a certain linear algebraic...
Fixed points of meromorphic solutions of higher order linear differential equations.
Fixed points of the derivative and -th power of solutions of complex linear differential equations in the unit disc.
Floquet theory for linear differential equations with meromorphic solutions.
Foliations with Degenerate Gauss maps on
We obtain a classification of codimension one holomorphic foliations on with degenerate Gauss maps.
Fonctions multiplicatives et équations différentielles
Fonctions multisommables
La notion de multisommabilité intervient dans la théorie des équations différentielles lorsque des exponentielles d’ordres différents se mélangent. Elle a été introduite par J. Écalle et étudié récemment par plusieurs auteurs. On en donne ici une définition simple, qui fait uniquement intervenir des propriétés de décroissance exponentielle.
From holonomy of the Ising model form factors to -fold integrals and the theory of elliptic curves.
Fuchsian differential equation for the perimeter generating function of three-choice polygons.
Galois properties of linear differential equations
Gauge-equivalent deformations of linear ordinary differential operators with constant coefficients.
Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)
We associate to any convenient nondegenerate Laurent polynomial on the complex torus a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of (or its universal unfolding) and of the corresponding Hodge theory.
General solution of overdamped Josephson junction equation in the case of phase-lock.
Generalization of Okamoto's equation to arbitrary Schlesinger system.
Generalized trigonometric functions in complex domain
We study extension of -trigonometric functions and to complex domain. For , the function satisfies the initial value problem which is equivalent to (*) in . In our recent paper, Girg, Kotrla (2014), we showed that is a real analytic function for on , where . This allows us to extend to complex domain by its Maclaurin series convergent on the disc . The question is whether this extensions satisfies (*) in the sense of differential equations in complex domain. This interesting...
Generating operator of or Gaudin transfer matrices has quasi-exponential kernel.