Action of an endomorphism on (the solutions of) a linear differential equation
[Action d’un endormorphisme sur (les solutions d’) une équation différentielle linéaire]
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 $\left(K,\partial \right)$ sur les solutions d’une équation différentielle linéaire à coefficients dans $\left(K,\partial \right)$. 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 $\left(K,\partial \right)$ on the solutions of a linear differential equation defined over $\left(K,\partial \right)$. After having introduced the theory, we give some concrete examples.

Reçu le :
Publié le :
DOI : https://doi.org/10.5802/pmb.28
Classification : 12H10,  12H20,  34M15
Mots clés : Differential Galois theory, discrete parameter, difference algebra
@article{PMB_2019___1_21_0,
author = {Lucia Di Vizio},
title = {Action of an endomorphism on (the solutions of) a linear differential equation},
journal = {Publications Math\'ematiques de Besan\c con - Alg\ebre et Th\'eorie des Nombres},
pages = {21--39},
publisher = {Presses universitaires de Franche-Comt\'e},
number = {1},
year = {2019},
doi = {10.5802/pmb.28},
language = {en},
url = {https://pmb.centre-mersenne.org/item/PMB_2019___1_21_0/}
}
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/item/PMB_2019___1_21_0/`

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