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Galois groups, Stokes operators and a theorem of Ramis. (English. Russian original) Zbl 0719.34013
Funct. Anal. Appl. 24, No. 4, 286-296 (1990); translation from Funkts. Anal. Prilozh. 24, No. 4, 31-42 (1990).
Let F be a field of germs of meromorphic functions at the origin, \(A\in M_ F(n)\) and (1) \(y'=Ay\) be a system of differential equations. J.-P. Ramis [C. R. Acad. Sci., Paris, Sér. I 301, 99-102 (1985; Zbl 0582.34006); ibid. 165-167 (1985; Zbl 0593.12005)] gave a sketch of proof of the following
Theorem. The Galois group of system (1) over F contains the Stokes transformations.
In the paper the authors obtain an alternative proof of the theorem which is based on a calculation of functional cochains. They advance also the hypothesis that the subgroup generated by Stokes and monodromy transformations is dense in the Galois group.

MSC:
34M99 Ordinary differential equations in the complex domain
12H05 Differential algebra
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[1] J. P. Ramis, ”Phénomène de Stokes et resommation,” C. R. Acad. Sci. Paris Sér. I Math.,301, No. 4, 99-102 (1985). · Zbl 0582.34006
[2] J. P. Ramis, ”Phénomène de Stokes et filtration de Gevrey sur le group de Picard-Vessiot,” C. R. Acad. Sci. Paris Sér. I Math., No. 5, 165-167 (1985). · Zbl 0593.12015
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