In the field of quantum chaos the main results are the following: derivation of the connection between the localization length of quantum chaos and classical diffusion rate (refs.[4,14,20,24,27]), analytical estimate for the time of applicability of quasiclassical expansion over classical trajectories for wave function in the chaotic regime (refs. [2,4]); establishment of the absence of local instability and of practical time reversibility of the quantum dynamics of the systems chaotic in the classical limit (refs. [3,14,21]), sharp increase of the localization length, or delocalization, for the 1d systems with time perturbation containing two or tree incommensurable frequencies and the connection of this phenomenon with Anderson localization in 2 and 3-dimensional solid state (refs. [14,27,37]), quantum delocalization of chaos in the kicked Harper model (ref.[51,52,57]), a quantum transition from localized to extended states for a ping-pong ball on an oscillating wall (ref. ).