Dynamics and statistics of quasi-energy levels for kicked quantum systems

We give a simple method of analysing the motion of (quasi)-energy levels of nonintegrable quantum systems when a nonintegrability parameter is changed. In both cases of autonomous systems and periodically kicked ones it offers a particularly simple explanation of the Hamiltonian character and complete integrability of the resulting equations of motion. In the case of kicked systems it allows for calculating the stationary distributions of quasi-energies