  Modelling the chaotic states in terms of the Gaussian Orthogonal Ensemble of
random matrices (GOE), we investigate the interaction of the GOE with regular
bound states. The eigenvalues of the latter may or may not be embedded in the
GOE spectrum. We derive a generalized form of the Pastur equation for the
average Green's function. We use that equation to study the average and the
variance of the shift of the regular states, their spreading width, and the
deformation of the GOE spectrum non-perturbatively. We compare our results with
various perturbative approaches.
