### Galois theory for nonlinear difference equations

Casale, G *(Rennes 1)*

Monday 11 May 2009, 16:30-17:30

Satellite

#### 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.

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