相关论文: On the Galois group some Fuchsian systems
We apply the difference-differential Galois theory developed by Hardouin and Singer to compute the differential-algebraic relations among the solutions to a second-order homogeneous linear difference equation of the form $…
The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular…
A categorical theory for the discretization of a large class of dynamical systems with variable coefficients is proposed. It is based on the existence of covariant functors between the Rota category of Galois differential algebras and…
We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations. With this we are able to reprove Hoelder's Theorem that the Gamma function satisfies no…
We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear…
We present a non-linear difference-differential equation whoes Galois group is a non-commutative and non-co-comutative Hopf algebra.
In this article we compute Galois groupoid of discret Painlev{\'e} equations. Our main tool is a semi-continuity theorem for the Galois groupoid in a confluence situation of a diffrence equation to a differential equation.
In this paper we develop a differential Galois theory for algebraic Lie-Vessiot systems in algebraic homogeneous spaces. Lie-Vessiot systems are non autonomous vector fields that are linear combinations with time-dependent coefficients of…
The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed.
The aim of this article is to provide a method to prove the irreducibility of non-linear ordinary differential equations by means of the differential Galois group of their variational equations along algebraic solutions. We show that if the…
We develop algorithms to compute the differential Galois group $G$ associated to a parameterized second-order homogeneous linear differential equation of the form \[ \tfrac{\partial^2}{\partial x^2} Y + r_1 \tfrac{\partial}{\partial x} Y +…
In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several…
This paper describes the classification of analytic $q$-difference equations. The difference Galois groups are computed. A tentative description of the universal difference Galois group is given.
We study the problem of solvability of linear differential systems with small coefficients in the Liouvillian sense (or, by generalized quadratures). For a general system, this problem is equivalent to that of solvability of the Lie algebra…
We develop a Galois theory for systems of linear difference equations with periodic parameters, for which we also introduce linear difference algebraic groups. We then apply this to constructively test if solutions of linear q-difference…
A Galois theory of differential fields with parameters is developed in a manner that generalizes Kolchin's theory. It is shown that all connected differential algebraic groups are Galois groups of some appropriate differential field…
We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field $\mathbb{C}(x)$ with derivation $\frac{d}{dx}$ and endomorphism $f(x)\mapsto f(x+1)$. Our main result is…
If we consider a q-analogue of linear differential equation, Galoois group of the q-analogue difference equation is still a linear algebraic group. Namely, by a quantization of linear differential equation, Galois group is not quantized. We…
We give a description of the rational representations of the differential Galois group of a Picard-Vessiot extension.
The classical Galois theory deals with certain finite algebraic extensions and establishes a bijective order reversing correspondence between the intermediate fields and the subgroups of a group of permutations called the Galois group of…