  The quantum-resonant evolution of the mean kinetic energy (MKE) of the kicked
particle is studied in detail on different time scales for {\em general}
kicking potentials. It is shown that the asymptotic time behavior of a
wave-packet MKE is typically a linear growth with bounded fluctuations having a
simple number-theoretical origin. For a large class of wave packets, the MKE is
shown to be exactly the superposition of its asymptotic behavior and transient
logarithmic corrections. Both fluctuations and transients can be significant
for not too large times but they may vanish identically under some conditions.
In the case of incoherent mixtures of plane waves, it is shown that the MKE
never exhibits asymptotic fluctuations but transients usually occur.
