On a general difference Galois theory I
Annales de l'Institut Fourier, Volume 59 (2009) no. 7, pp. 2709-2732.

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.

La théorie de Picard-Vessiot aux différences, la théorie de Galois des équations aux différences linéaires, est bien connue. Nous proposons une théorie de Galois des équations aux différences générales qui généralise la théorie de Picard-Vessiot. Pour toute extension de corps aux différences de caractéristique 0, nous attachons son groupe de Galois qui est un groupe de transformations de coordonnées.

Received:
Accepted:
DOI: 10.5802/aif.2505
Classification: 12Hxx,  37Fxx,  58Hxx,  14Hxx
Keywords: General difference Galois theory, dynamical system, integrable dynamical system, Galois groupoid
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Morikawa, Shuji. On a general difference Galois theory I. Annales de l'Institut Fourier, Volume 59 (2009) no. 7, pp. 2709-2732. doi : 10.5802/aif.2505. https://aif.centre-mersenne.org/articles/10.5802/aif.2505/

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