AI 中文总结
本文针对系数矩阵为$Ax+B$的线性$q$-差分系统，构造典范基本解、建立等单值性理论，推导单值性数据显式公式，证明其$q\ o1$的微分极限对应微分系统的相关结构。
AI 中文摘要
本文针对系数矩阵为$Ax+B$的线性$q$-差分系统构造了典范基本解，建立了对应的等单值性理论，并研究了当$q\ o1$时的微分极限。我们确定了一般等单值形变的渐近行为，根据其渐近主项推导了单值性数据的显式公式，还证明了当$q\ o1$时的微分极限可恢复对应微分系统的典范基本解、单值性数据及等单值形变。
英文摘要
In this paper, we construct canonical fundamental solutions for linear $q$-difference systems with coefficient matrix $Ax+B$, develop the associated isomonodromy theory, and study the differential limit as $q\to1$. We determine the asymptotic behavior of generic isomonodromic deformations, and derive explicit formulas for their monodromy data in terms of their asymptotic leading terms. We also show that the differential limit as $q\to1$ recovers the canonical fundamental solutions, the monodromy data, and the isomonodromic deformations of the corresponding differential systems.
Comments58 pages, 1 figure
