  We study the resonances of the quantum kicked rotor subjected to an extended
initial distribution. For the primary resonances we obtain the dispersion
relation for the map of this system. We find an analytical dependence of the
statistical moments on the shape of the initial distribution. For the secondary
resonances we obtain numerically a similar dependence. This allows us to devise
an extended initial condition which produces an average angular momentum
pointing in a preset direction which increases with time with a preset ratio.
