A Characterization of Linear Difference Equations Which are Solvable by Elementary Operations.
A note on differentially algebraic solutions of first order linear difference equations.
An invariant for difference field extensions
In this paper we introduce a new invariant for extensions of difference fields, the distant degree, and discuss its properties.
Automatique en temps discret et algèbre aux différences.
Différentielles non commutatives et théorie de Galois différentielle ou aux différences
Frobenius modules and Galois representations
Frobenius modules are difference modules with respect to a Frobenius operator. Here we show that over non-archimedean complete differential fields Frobenius modules define differential modules with the same Picard-Vessiot ring and the same Galois group schemes up to extension by constants. Moreover, these Frobenius modules are classified by unramified Galois representations over the base field. This leads among others to the solution of the inverse differential Galois problem for -adic differential...
Galois groups and connection matrices for -difference equations.
Galois theory of fuchsian q-difference equations
Galois theory of -difference equations
Choose with . The main theme of this paper is the study of linear -difference equations over the field of germs of meromorphic functions at . A systematic treatment of classification and moduli is developed. It turns out that a difference module over induces in a functorial way a vector bundle on the Tate curve that was known for modules with ”integer slopes“, [Saul, 2]). As a corollary one rediscovers Atiyah’s classification of the indecomposable vector bundles on the complex Tate...
Lemmes de Hensel pour les opérateurs différentiels et les opérateurs aux différences
Les dérivées sur un corps valué non archimédien
Linearly Reducible Difference Operators (Short Communication)
Linearly Reducible Linear Difference Operators
On a general difference Galois theory I
We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic , we attach its Galois group, which is a group of coordinate transformation.
On a general difference Galois theory II
We apply the General Galois Theory of difference equations introduced in the first part to concrete examples. The General Galois Theory allows us to define a discrete dynamical system being infinitesimally solvable, which is a finer notion than being integrable. We determine all the infinitesimally solvable discrete dynamical systems on the compact Riemann surfaces.
On the Galois theory of difference fields.
Picard-Vessiot theory in general Galois theory
We give a transparent proof that difference Picard-Vessiot theory is a part of the general difference Galois theory. We apply the proof to iterative q-difference Picard-Vessiot theory to show that Picard-Vessiot theory for iterative q-difference field extensions is in the scope of the general Galois theory of Heiderich. We also show that Picard-Vessiot theory is commutative in the sense that studying linear difference-differential equations, no matter how twisted the operators are, we cannot encounter...
Polynômes de Barsky
Propriétés algébriques de suites différentiellement finies
Reducible Linear Difference Operators