2002/11/01 by Jacques Sauloy, Sauloy, Jacques
Computer Science · Mathematics · Physics and Astronomy · #05A30 - 33D - 39A10 - 58F #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Quantum Algebra (math.QA) #math.QA #msc:05A30 #msc:33D #msc:39A10 #msc:58F
paper · pdf · doi:10.48550/arxiv.math/0211007
113 pages. Prepublications du Laboratoire Emile Picard n. 148. See also http://picard.ups-tlse.fr
arxiv created 2002/11/01 · openalex publication_date 2002/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
G.D. Birkhoff extended the classical Riemann-Hilbert problem for differential equations to the case of ``fuchsian'' linear q-difference systems with rational coefficients. He solved it in the generic case: the classifying object which he introduces is made up of the connection matrix P, together with the exponents at 0 and ∞. We follow his method in the general case, but treat symetrically 0 and ∞ and use no ``wildly'' growing solutions. When q tends to 1, P tends to a locally constant matrix P such that the (finitely many) values P(a)-1P(b) are the monodromy matrices of the limiting differential system (assumed to be non resonant at 0 and ∞) at the singularities on C*. This text is that of preprint 148 of the Laboratoire Emile Picard (february 1999). A shorter version was published by the Annales de l'Institut Fourier, 50, 4, (2000).