  We study the intermediate statistics of the spectrum of quasi-energies and of
the eigenfunctions in the kicked rotator, in the case when the corresponding
system is fully chaotic while quantally localized. As for the eigenphases, we
find clear evidence that the spectral statistics is well described by the Brody
distribution, notably better than by the Izrailev's one, which has been
proposed and used broadly to describe such cases. We also studied the
eigenfunctions of the Floquet operator and their localization. We show the
existence of a scaling law between the repulsion parameter with relative
localization length, but only as a first order approximation, since another
parameter plays a role. We believe and have evidence that a similar analysis
applies in time-independent Hamilton systems.
