A technique for generating Rydberg wavepackets in preferred target states i
s demonstrated that exploits the mixed phase space structure of the periodi
cally 'kicked' Rydberg atom. Experimental data and classical simulations fo
r very-high-n Rydberg atoms are presented that show that application of a t
rain of equispaced, unidirectional half-cycle pulses can lead to localizati
on of the final wavepacket in classical stable islands. The product wavepac
kets are examined using a delayed half-cycle probe pulse. It is demonstrate
d that the motion of the wavepackets is either quasiperiodic or random depe
nding on whether or not the initial state of the atom overlaps a stable isl
and.