论文标题
可降低方程的矩阵，具有两个不规则的庞加尔等级1的矩阵，这是通过可还原的heun型方程的单片矩阵
Stokes matrices of a reducible equation with two irregular singularities of Poincaré rank 1 via monodromy matrices of a reducible Heun type equation
论文作者
论文摘要
我们考虑一个二阶可还原方程，其非谐波不规则奇异性为$ x = 0 $和$ x = \ infty $。他们俩都是庞加莱排名1的。我们引入了一个小的复杂参数$ \ varepsilon $，将$ x = 0 $和$ x = \ iftty $分配到四个不同的fuchsian奇异界$ x_l = - \ sqrt {\ sqrt {\ varepsilon} $ x_ {ll} = -1/\ sqrt {\ varepsilon}，x_ {rr} = 1/\ sqrt {\ varepsilon} $，分别为。扰动的方程是具有4个不同奇异性的二阶降低紫红色方程，即Heun型方程。然后，我们证明，当扰动方程完全具有不同类型的两个谐振奇点时，当$ \ varepsilon \ rightarrow 0 $ 0以真实的正方向为$ \ VAREPSILON \ rightarrow 0时，初始方程的所有stokes矩阵都被视为效率方程式矩阵的nilpotent部分的限制。为了确定这一结果，我们将直接计算与理论方法结合在一起。
We consider a second order reducible equation having non-resonant irregular singularities at $x=0$ and $x=\infty$. Both of them are of Poincaré rank 1. We introduce a small complex parameter $\varepsilon$ that splits together $x=0$ and $x=\infty$ into four different Fuchsian singularities $x_L=-\sqrt{\varepsilon}, x_R=\sqrt{\varepsilon}$ and $x_{LL}=-1/\sqrt{\varepsilon}, x_{RR}=1/\sqrt{\varepsilon}$, respectively. The perturbed equation is a second order reducible Fuchsian equation with 4 different singularities, i.e. a Heun type equation. Then we prove that when the perturbed equation has exactly two resonant singularities of different type, all the Stokes matrices of the initial equation are realized as a limit of the nilpotent parts of the monodromy matrices of the perturbed equation when $\varepsilon \rightarrow 0$ in the real positive direction. To establish this result we combine a direct computation with a theoretical approach.
