常系数线性系(yx)'=(cdab)(yx)具有指数型二分性(特征根一正一负)的充要条件是ad-bc<0.本文说明概周期线性系(yx)'=(a(t)d(t)a(t)b(t))(yx)当a(t)d(t)-b(t)c(t)<0时,一般也有指数型二分性.同时给出特征数较准确的估计.

Autonomous linear equation (yx)'=(cd ab)(yx) has an exponential dichotomy (has a positive eigenvalue and a negative eigenvalue) if and only if ad-bc < 0. In this paper, we show that, if a(t)d(t) - b(t)c(t) < 0, almost periodic linear system ( yx ) = (c(t)d(t) a(t)b(t)) (yx) usually has an exponential dichotomy, and give relatively exact estimates for characteristic numbers.