艾里方程的斯托克斯矩阵

IF 0.4 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal Pub Date : 2021-03-30 DOI:10.2748/tmj.20210506

A. Hohl, Konstantin Jakob

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引用次数: 1

摘要

我们计算了广义Airy方程的Stokes矩阵，并证明了它们是正则单势的（直到与形式的单调相乘）。这类微分方程由Katz定义，包括经典的Airy方程。此外，它还包括非刚性的微分方程。我们的方法基于由D’Agnolo、Hien、Morando和Sabbah引起的反常sheaf的增强傅立叶-萨托变换的Stokes矩阵的拓扑计算。

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Stokes matrices for Airy equations

We compute Stokes matrices for generalised Airy equations and prove that they are regular unipotent (up to multiplication with the formal monodromy). This class of differential equations was defined by Katz and includes the classical Airy equation. In addition, it includes differential equations which are not rigid. Our approach is based on the topological computation of Stokes matrices of the enhanced Fourier-Sato transform of a perverse sheaf due to D'Agnolo, Hien, Morando and Sabbah.

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