Abstract
This chapter presents some recent results in the asymptotic integration of linear differential systems. The stability and asymptotic behavior of solutions of an autonomous linear differential system x' = Ax are determined by the spectrum of the constant matrix A. If B(t) is a suitably small perturbation, then the stability and asymptotic behavior of solutions of x' = [A + B (t)]x are still determined by the limiting system x' = Ax. The essence of the method employed by Harris–Lutz is the transformation of the original differential system into one to which the fundamental result of Levinson Hartman–Wintner applies. The germ of this method has been utilized recently by Harris–Lutz to give a unified treatment of asymptotic integration of linear differential systems through transformation into L-diagonal canonical form and the fundamental result of Levinson.
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