DIS

Abstract

I will present Malgrange's definition of Galois pseudogroup for a nonlinear difference equation and explaine how it can be used to obtain integrability condition on linearisation of the equation. In case of a symplectique map one gets the discrete version of Morales-Ramis theorem : If such a map is Liouville integrable then the difference Galois group of its linearisation along a (good) particular solution is almost commutative.