Perturbations of Jordan Differential Systems

Abstract

Whereas in Chaps. 2 and 4, we studied the asymptotic behavior of solutions of perturbations of diagonal systems of differential equations, we are now interested in the asymptotic behavior of solutions of systems of the form

$$\displaystyle{ y^{{\prime}} = \left [J(t) + R(t)\right ]y(t)t \geq t_{ 0}, }$$

(6.1)

where J(t) is now in Jordan form and R(t) is again a perturbation. Early results on perturbations of constant Jordan blocks include works by Dunkel [50] and Hartman–Wintner [73]. The focus here is an approach, developed by Coppel and Eastham, to reduce perturbed Jordan systems to a situation where Levinson’s fundamental theorem can be applied.