Asymptotic analysis for hypergeometric systems and Garnier systems

为了将精确WKB分析推广到多维问题，我们从精确WKB分析的角度考虑了完全可积系统，如超几何系统和Garnier系统。我们得到以下基本结果：“转向点合并现象”在确定完全可积系统的Stokes几何中起着重要的作用，作为其限制条件得到的高阶常微分方程也是如此，在线性完全可积系统的情况下，Pearcey系统给出了转向点合并现象发生点处的标准形，关于精确WKB分析理论的巩固，我们还利用差分方程的方法对线性方程和Painleve方程的Voros系数进行了分析，取得了很大的进展。

To generalize the exact WKB analysis to multidimensional problems, we consider completely integrable systems such as hypergeometric systems and Garnier systems from the viewpoint of the exact WKB analysis. We obtain the following fundamental results: "Coalescing phenomena of turning points" play an important role in determining the Stokes geometry of completely integrable systems as well as of higher order ordinary differential equations obtained as their restriction, in the case of linear completely integrable systems the Pearcey system gives a normal form at a point where a coalescing phenomenon of turning points occurs, and so on. Concerning the consolidation of the theory of exact WKB analysis, we also make a big progress in the analysis of the Voros coefficients of linear equations and Painleve equations by using the method of difference equations.