2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57088The eigenvector expansion developed in the preceding paper for a system of damped linear oscillators is extended to critical points, where eigenvectors merge and the time-evolution operator $H$ assumes a Jordan-block structure. The representation of the bilinear map is obtained in this basis. Perturbations $εΔH$ around an $M$-th order critical point generically lead to eigenvalue shifts $\simε^{1/M}$ dependent on only_one_ matrix element, with the $M$ eigenvalues splitting in equiangular directions in the complex plane. Small denominators near criticality are shown to cancel.REVTeX4, 9pp., 5 PS figures. v2: extensive streamliningMathematical PhysicsDynamical SystemsRings and AlgebrasClassical Physicstext