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We study the intermediate statistics of the spectrum of quasi-energies and ofthe eigenfunctions in the kicked rotator, in the case when the correspondingsystem is fully chaotic while quantally localized. As for the eigenphases, wefind clear evidence that the spectral statistics is well described by the Brodydistribution, notably better than by the Izrailev's one, which has beenproposed and used broadly to describe such cases. We also studied theeigenfunctions of the Floquet operator and their localization. We show theexistence of a scaling law between the repulsion parameter with relativelocalization length, but only as a first order approximation, since anotherparameter plays a role. We believe and have evidence that a similar analysisapplies in time-independent Hamilton systems.

Dynamical localization in kicked rotator as a paradigm of other systems: spectral statistics and the localization measure