  For manifolds Euclidian at infinity and compact perturbations of the
Laplacian, we show that under assumptions involving hyperbolicity of the
classical flow on the trapped set and its period spectrum, there are strips
below the real axis where the resonance counting function grows sub-linearly.
We also provide an inverse result, showing that the knowledge of the scattering
poles can give some information about the Hausdorff dimension of the trapped
set when the classical flow satisfies the Axiom-A condition.
