The space of monodromy data for the Jimbo–Sakai family of $q$-difference equations

Yousuke Ohyama; Jean-Pierre Ramis; Jacques Sauloy

doi:10.5802/afst.1659

The space of monodromy data for the Jimbo–Sakai family of

q

-difference equations

Yousuke Ohyama ¹ ; Jean-Pierre Ramis ² ; Jacques Sauloy ³

¹ Department of Mathematical Sciences, Tokushima University, 2-1 Minamijyousanjima-cho, Tokushima 770-8506, Japan
² Institut de France (Académie des Sciences) and Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université Paul Sabatier (Toulouse 3), 118 route de Narbonne, 31062 Toulouse CEDEX 9, France
³ Toulouse

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 5, pp. 1119-1250.

Résumé
Abstract

Nous formulons une correspondance de Riemann–Hilbert géométrique qui s’applique à la dérivation par Jimbo et Sakai de l’équation $q$ -PVI à partir de conditions « d’isomonodromie ». C’est une étape d’un travail en cours en vue de l’application de la $q$ -isomonodromie et des $q$ -isoStokes à $q$ -Painlevé.

We formulate a geometric Riemann–Hilbert correspondence that applies to the derivation by Jimbo and Sakai of equation $q$ -PVI from “isomonodromy” conditions. This is a step within work in progress towards the application of $q$ -isomonodromy and $q$ -isoStokes to $q$ -Painlevé.

Publié le : 2021-04-12

DOI : 10.5802/afst.1659

Affiliations des auteurs :

Yousuke Ohyama ¹ ; Jean-Pierre Ramis ² ; Jacques Sauloy ³

¹ Department of Mathematical Sciences, Tokushima University, 2-1 Minamijyousanjima-cho, Tokushima 770-8506, Japan
² Institut de France (Académie des Sciences) and Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université Paul Sabatier (Toulouse 3), 118 route de Narbonne, 31062 Toulouse CEDEX 9, France
³ Toulouse

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Yousuke Ohyama; Jean-Pierre Ramis; Jacques Sauloy. The space of monodromy data for the Jimbo–Sakai family of $q$-difference equations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 5, pp. 1119-1250. doi : 10.5802/afst.1659. https://afst.centre-mersenne.org/articles/10.5802/afst.1659/

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