  We find the Weyl law followed by the eigenvalues of contractive maps. An
important property is that it is mainly insensitive to the dimension of the
corresponding invariant classical set, the strange attractor. The usual
explanation for the fractal Weyl law emergence in scattering systems (i.e.,
having a projective opening) is based on classical phase space distributions
evolved up to the quantum to classical correspondence (Ehrenfest) time. In the
contractive case this reasoning fails to describe it. Instead, we conjecture
that the support for this behavior is essentially given by the strong
non-orthogonality of the eigenvectors of the contractive superoperator.
