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. [46]).