  A quantum manifestation of chaotic classical dynamics is found in the
framework of oscillatory numbers statistics for the model of nonlinear
dissipative oscillator. It is shown by numerical simulation of an ensemble of
quantum trajectories that the probability distributions and variances of
oscillatory number states are strongly transformed in the order-to-chaos
transition. The nonclassical, sub-Poissonian statistics of oscillatory
excitation numbers is established for chaotic dissipative dynamics in the
framework of Fano factor and Wigner functions. These results are proposed for
testing and experimental studing of quantum dissipative chaos.
