Galois groupoid and confluence of difference equations

TL;DR

This paper computes the Galois groupoid of discrete Painlevé equations using a semi-continuity theorem, linking difference and differential equations to understand their symmetries and confluence behavior.

Contribution

It introduces a semi-continuity theorem for Galois groupoids in confluence scenarios, advancing the understanding of symmetries in difference and differential equations.

Findings

Galois groupoid of discrete Painlevé equations computed

Semi-continuity theorem established for confluence cases

Enhanced understanding of symmetries in difference-differential equations

Abstract

In this article we compute Galois groupoid of discret Painlev{\'e} equations. Our main tool is a semi-continuity theorem for the Galois groupoid in a confluence situation of a diffrence equation to a differential equation.