Action of an endomorphism on (the solutions of) a linear differential equation

Lucia Di Vizio

doi:10.5802/pmb.28

Action of an endomorphism on (the solutions of) a linear differential equation
[Action d’un endormorphisme sur (les solutions d’) une équation différentielle linéaire]

Lucia Di Vizio ¹

¹ Laboratoire de Mathématiques, UVSQ, 45 avenue des États-Unis 78035 Versailles cedex, France

Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2019), pp. 21-39.

Résumé
Abstract

Le but de ce survol est de présenter d’une façon accessible le contenu des articles [8] et [9], qui donnent une description galoisienne de l’action d’un endomorphisme d’un corps différentiel $(K, \partial)$ sur les solutions d’une équation différentielle linéaire à coefficients dans $(K, \partial)$ . Après une présentation de la théorie nous donnons quelques exemples d’applications.

The purpose of this survey is to provide the reader with a user friendly introduction to the two articles [8] and [9], which give a Galoisian description of the action of an endomorphism of a differential field $(K, \partial)$ on the solutions of a linear differential equation defined over $(K, \partial)$ . After having introduced the theory, we give some concrete examples.

Reçu le : 2018-01-04
Publié le : 2019-10-15

DOI : 10.5802/pmb.28

Classification : 12H10, 12H20, 34M15
Mots clés : Differential Galois theory, discrete parameter, difference algebra

Affiliations des auteurs :

Lucia Di Vizio ¹

¹ Laboratoire de Mathématiques, UVSQ, 45 avenue des États-Unis 78035 Versailles cedex, France

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Lucia Di Vizio. Action of an endomorphism on (the solutions of) a linear differential equation. Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2019), pp. 21-39. doi : 10.5802/pmb.28. https://pmb.centre-mersenne.org/articles/10.5802/pmb.28/

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Algèbre et Théorie des Nombres