More on linear differential systems with small delays

We'll study the aysymptotic dynamics of linear systems of DDEs with small delays. It can be shown that asymptotically such systems behave as the so-called special solutions and for linear DDEs these solutions coincide with fundamental solutions. Moreover, we are able to calculate the limitof X^{-1}(t)x(f)(t) as t tends to infinity, where X(t) is the fundamental matrix (a special solution matrix) and x(f) is the solution to DDe with the initial function f at t=0. This limit can be expressed in terms of the basis of the generalised eigenspace for the formal adjoint equation.