Sauloy, Jacques The connection matrix of a \(q\)-difference system confluent to a differential system and the monodromy matrices. (Matrice de connexion d’un système aux \(q\)-différences confluant vers un système différentiel et matrices de monodromie.) (French. Abridged English version) Zbl 0919.39004 C. R. Acad. Sci., Paris, Sér. I, Math. 328, No. 2, 155-160 (1999). Summary: We built in the preceding paper [ibid. 328, No. 1, 51-52 (1999; Zbl 0919.39003)] a version with elliptic coefficients of the Birkhoff connection matrix and showed its role in the classification of regular singular \(q\)-difference systems. We give here a geometrical interpretation: when \(q\) tends to 1, \(P\) tends to a locally constant matrix \(\widetilde{P}\) such that the (finitely many) values \(\widetilde{P}(a)^{-1} \widetilde{P}(b)\) are the monodromy matrices of the limiting differential system (assumed to be non-resonant at 0 and \(\infty\)) at the singularities on \(\mathbb{C}^*\). Cited in 2 Documents MSC: 39A12 Discrete version of topics in analysis 39A10 Additive difference equations Keywords:elliptic coefficients; Birkhoff connection matrix; regular singular \(q\)-difference systems; monodromy matrices; limiting differential system Citations:Zbl 0919.39003 PDFBibTeX XMLCite \textit{J. Sauloy}, C. R. Acad. Sci., Paris, Sér. I, Math. 328, No. 2, 155--160 (1999; Zbl 0919.39004) Full Text: DOI