Systèmes aux q-différences singuliers réguliers: solutions canoniques, classification, matrice de connexion et monodromie
| dc.creator | Sauloy, Jacques | |
| dc.date | 2002-11-01 | |
| dc.date.accessioned | 2026-07-07T04:52:33Z | |
| dc.date.available | 2026-07-07T04:52:33Z | |
| dc.description | 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 $\infty$. 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.description | 113 pages. Prepublications du Laboratoire Emile Picard n. 148. See also http://picard.ups-tlse.fr | |
| dc.identifier | https://arxiv.org/abs/math/0211007 | |
| dc.identifier | http://arxiv.org/abs/math/0211007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65504 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 05A30 - 33D - 39A10 - 58F | |
| dc.title | Systèmes aux q-différences singuliers réguliers: solutions canoniques, classification, matrice de connexion et monodromie | |
| dc.type | text |