Darboux-Lamé equation and isomonodromic deformation.
Das Existenzproblem multivalenter Lösungen bei Differentialgleichungen.
Déformations isomonodromiques, forme de Liouville, fonction
Cet article améliore des résultats antérieurs de Miwa et de l’auteur sur la “fonction ” de l’équation de Schlesinger. On relie cette fonction à la forme de Liouville d’un groupe de lacets associé naturellement à cette équation
Diagonalization and rationalization of algebraic Laurent series
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...
Die allgemeine Lösung einer zylindrischen Differentialgleichung vierter Ordnung nullten Parameterwertes
Die Lösung der linearen Differentialgleichung 2. Ordnung um zwei einfache Singularitäten durch Reihen nach hypergeometrischen Funktionen.
Diferenciální rovnice v komplexním oboru [Book]
Diferenciální rovnice v reálném oboru [Book]
Differential analogues of the Brück conjecture
We give some growth properties for solutions of linear complex differential equations which are closely related to the Brück Conjecture. We also prove that the Brück Conjecture holds when certain proximity functions are relatively small.
Differential equations on the plane with given solutions.
The aim of this paper is to construct the analytic vector fields with given as trajectories or solutions. In particular we construct the polynomial vector field from given conics (ellipses, hyperbola, parabola, straight lines) and determine the differential equations from a finite number of solutions.
Diskonjugierte Differentialgleichungen 2. Ordnung im Komplexen.
Diskonjugiertheit und k-Diskonjugiertheit von w(n) + f(x)w = 0 bei komplexwertigem f.
Diskonjugovaná a nekritická komplexná diferenciálna rovnica
Distributional and entire solutions of ordinary differential and functional differential equations.
Divergence and summability of normal forms of systems of differential equations with nilpotent linear part
Domaines de linearisation asymptotique pour des champs de vecteurs.
Double exponential estimate for the number of zeros of complete Abelian integrals and rational envelopes of linear ordinary differential equations with an irreducible monodromy group.
Dynamics on Character Varieties and Malgrange irreducibility of Painlevé VI equation
We consider representations of the fundamental group of the four punctured sphere into . The moduli space of representations modulo conjugacy is the character variety. The Mapping Class Group of the punctured sphere acts on this space by symplectic polynomial automorphisms. This dynamical system can be interpreted as the monodromy of the Painlevé VI equation. Infinite bounded orbits are characterized: they come from -representations. We prove the absence of invariant affine structure (and invariant...
Dynamique et formes normales d’équations différentielles implicites
Dans cet article on cherche à comprendre la dynamique locale d’équations différentielles implicites de la forme , où est un germe de fonction sur (où ou ), au voisinage d’un point singulier. Pour cela on utilise la relation intime entre les systèmes implicites et les champs liouvilliens. La classification par transformation de contact des équations implicites provient de la classification symplectique des champs liouvilliens. On utilise alors toute la théorie des formes normales pour les...