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On a general difference Galois theory I

Shuji Morikawa (2009)

Annales de l’institut Fourier

We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic 0 , we attach its Galois group, which is a group of coordinate transformation.

On a general difference Galois theory II

Shuji Morikawa, Hiroshi Umemura (2009)

Annales de l’institut Fourier

We apply the General Galois Theory of difference equations introduced in the first part to concrete examples. The General Galois Theory allows us to define a discrete dynamical system being infinitesimally solvable, which is a finer notion than being integrable. We determine all the infinitesimally solvable discrete dynamical systems on the compact Riemann surfaces.

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