The intermediate level statistics in dynamically localized chaotic eigenstates

We demonstrate that the energy or quasienergy level spacing distribution in dynamically localized chaotic eigenstates is excellently described by the Brody distribution, displaying the fractional power law level repulsion. This we show in two paradigmatic systems, namely for the fully chaotic eigenstates of the kicked rotator at K=7, and for the chaotic eigenstates in the mixed-type billiard system (Robnik 1983), after separating the regular and chaotic eigenstates by means of the Poincar\'e Husimi function, at very high energies with great statistical significance (587654 eigenstates, starting at about 1.000.000 above the ground state). This separation confirms the Berry-Robnik picture, and is performed for the first time at such high energies.