  We show that the mechanism of quantum freeze of fidelity decay for
perturbations with zero time-average, recently discovered for a specific case
of integrable dynamics [New J. Phys. 5 (2003) 109], can be generalized to
arbitrary quantum dynamics. We work out explicitly the case of chaotic
classical counterpart, for which we find semi-classical expressions for the
value and the range of the plateau of fidelity. After the plateau ends, we find
explicit expressions for the asymptotic decay, which can be exponential or
Gaussian depending on the ratio of the Heisenberg time to the decay time.
Arbitrary initial states can be considered, e.g. we discuss coherent states and
random states.
