  An exact semiclassical version of the classical KAM theorem about small
perturbations of vector fields on the torus is given. Moreover, a
renormalization theorem based on counterterms for some semiclassical systems
that are close to being completely integrable is obtained. We apply these
results to characterize the sets of semiclassical measures and quantum limits
for sequences of $L^2$-eigenfunctions of these systems.
