  Using the quantum trajectories approach we study the quantum dynamics of a
dissipative chaotic system described by the Zaslavsky map. For strong
dissipation the quantum wave function in the phase space collapses onto a
compact packet which follows classical chaotic dynamics and whose area is
proportional to the Planck constant. At weak dissipation the exponential
instability of quantum dynamics on the Ehrenfest time scale dominates and leads
to wave packet explosion. The transition from collapse to explosion takes place
when the dissipation time scale exceeds the Ehrenfest time. For integrable
nonlinear dynamics the explosion practically disappears leaving place to
collapse.
