Systèmes aux q-différences singuliers réguliers: solutions canoniques, classification, matrice de connexion et monodromie

dc.creatorSauloy, Jacques
dc.date2002-11-01
dc.date.accessioned2026-07-07T04:52:33Z
dc.date.available2026-07-07T04:52:33Z
dc.descriptionG.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 $\infty$. We follow his method in the general case, but treat symetrically 0 and $\infty$ and use no ``wildly'' growing solutions. When $q$ tends to 1, $P$ tends to a locally constant matrix $\tilde{P}$ such that the (finitely many) values $\tilde{P}(a)^{-1}\tilde{P}(b)$ are the monodromy matrices of the limiting differential system (assumed to be non resonant at 0 and $\infty$) at the singularities on $\mathbf{C}^{*}$. 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).
dc.description113 pages. Prepublications du Laboratoire Emile Picard n. 148. See also http://picard.ups-tlse.fr
dc.identifierhttps://arxiv.org/abs/math/0211007
dc.identifierhttp://arxiv.org/abs/math/0211007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65504
dc.subjectQuantum Algebra
dc.subject05A30 - 33D - 39A10 - 58F
dc.titleSystèmes aux q-différences singuliers réguliers: solutions canoniques, classification, matrice de connexion et monodromie
dc.typetext

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