Normally hyperbolic smooth trapped sets are structurally
stable and occur in many interesting situations: for instance
for Kerr black hole metrics. We show that the corresponding
semiclassical resonances (e.g. quasinormal modes for Kerr
black holes) are separated from the real axis which has
consequences for decay of waves and other phenomena.

The proof is a simple example of techniques
used in the semiclassical study of quantum resonances
and I hope to present it in a self-contained way.