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

Di Vizio, Lucia

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

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.

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

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