系统aux q-差分奇异规则：解决方案规范，分类，矩阵的连接和monodromie
Systèmes aux q-différences singuliers réguliers: solutions canoniques, classification, matrice de connexion et monodromie
摘要：
G.D. Birkhoff将微分方程的经典黎曼-希尔伯特问题扩展到具有有理系数的“fuchsian”线性$q$ -差分系统的情况。他解决了它在一般情况下：分类对象，他介绍的是由连接矩阵$P$，连同指数在0和$\infty$。我们在一般情况下遵循他的方法，但对称地处理0和$\infty$，并且不使用“疯狂”增长的解决方案。当$q$趋向于1时，$P$趋向于局部常数矩阵$\tilde{P}$，使得（多个）值$\tilde{P}(a)^{-1}\tilde{P}(b)$是极限微分系统（假设在0和$\infty$处非共振）在$\mathbf{C}^{*}$上奇点处的单值矩阵。这段文字是埃米尔·皮卡德出版社（1999年2月）的预印本148。较短的版本由Annales de l 'Institut Fourier出版，50，4，（2000）。
英文摘要：
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).
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