hal-00128274, version 1

On the generalized Riemann-Hilbert problem with irregular singularities

A. A. Bolibruch, Stéphane Malek, Claude Mitschi ¹

(2004)

• 1:  Institut de Recherche Mathématique Avancée (IRMA)
• http://www-irma.u-strasbg.fr/
  CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I 7 rue René-Descartes, 67084 Strasbourg Cedex, France France

Bibliographic reference

• Type of document: Documents without publication reference (Preprint)
• Subject:

  Mathematics/Classical Analysis and ODEs

  Mathematics/Algebraic Geometry

• Title: On the generalized Riemann-Hilbert problem with irregular singularities
• Abstract: 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.
• Fulltext language: English
• Production date: 2004
• Keyword(s): système différentiel linéaire ordinaire – singularité irrégulière – monodromie – matrice de Stokes – rang de Poincaré – fibré vectoriel – connexion méromorphe – groupe de galois différentiel
• Classification: 34M50, 34M25,34M35,34M40,20G15

• hal-00128274, version 1
• http://hal.archives-ouvertes.fr/hal-00128274
• oai:hal.archives-ouvertes.fr:hal-00128274
• From: Véronique Bertrand <>
• Submitted on: Wednesday, 31 January 2007 15:03:36
• Updated on: Thursday, 1 February 2007 10:12:28