We give sufficient conditions, on data including the monodromy representation, the Stokes matrices and the Poincare ranks at prescribed singularities, to solve the generalized Riemann-Hilbert problem with irregular singularities. We recover in particular the irreducibility condition on the monodromy given by Bolibrukh and Kostov in the classical case. We apply the above criteria to solve the inverse problem in differential Galois theory with a better control of the singularities.
Publié le : 2004-07-05
Classification:
système différentiel linéaire ordinaire,
singularité irrégulière,
monodromie,
matrice de Stokes,
rang de Poincaré,
fibré vectoriel,
connexion méromorphe,
groupe de galois différentiel,
34M50, 34M25,34M35,34M40,20G15,
[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA],
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
@article{hal-00128274,
author = {Bolibruch, A. A. and Malek, St\'ephane and Mitschi, Claude},
title = {On the generalized Riemann-Hilbert problem with irregular singularities},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00128274}
}
Bolibruch, A. A.; Malek, Stéphane; Mitschi, Claude. On the generalized Riemann-Hilbert problem with irregular singularities. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00128274/