Irregularity for Singular System of Ordinary Differential Equations in Complex Domain

Abstract

An irregularity of an ordinary differential equation with an irregular singular point is defined by the maximal rate of exponential growth of all solutions of the associated homogeneous equation. We shall study first order singular systems of Poincaré rank p (≥ 0) and characterize its irregularity from two different viewpoints; the first one is from the order of zeros of coefficient matrices, and the second one is from the comparison of indices of the system on formal Gevrey spaces.