2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156181We consider a semi-classical completely integrable system defined by a $\hbar$-pseudodifferential operator $\hat{H}$ on the torus $\mathbb{T}^{d}$. In order to study perturbed operators of the form $\hat{H}+\hbar^κ\hat{K}$, where $\hat{K}$ is an arbitrary pseudodifferential operator and $κ>0$, we prove the conjugacy to a suitable normal form. This is then used to construct a large number of quasimodes.One mistake in Proposition 15 corrected, introduction shortened, typographics errors fixed, bibliography updatedMathematical Physicstext