Solution of central and side coupling problems for certain systems of three equations (Q1337843)

In the complex domain a system of differential equations (1) \(dw/dz = (A_ 0 + A_{-1} z^{-1}) w\), \(z \in\mathbb{C}\), \(w \in\mathbb{C}^ 3\), and a third-order equation of same type are considered. Here \(A_ 0 = \text{diag} (\lambda_ 1, \lambda_ 2, \lambda_ 3)\) and \(A_{-1}\) are constant matrices, \(\lambda_ 1 \neq \lambda_ 2 \neq \lambda_ 3\). For different values of \(A_ 0\) and \(A_{-1}\) the author gives matrices connecting asymptotic decompositions of fundamental matrix solutions of (1) in different sectors of the complex plane.