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Galois theory for nonlinear difference equations

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Discrete Integrable Systems

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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