  The effect of pulse train noise on the quantum resonance peaks of the Atom
Optics Kicked Rotor is investigated experimentally. Quantum resonance peaks in
the late time mean energy of the atoms are found to be surprisingly robust
against all levels of noise applied to the kicking amplitude, whilst even small
levels of noise on the kicking period lead to their destruction. The robustness
to amplitude noise of the resonance peak and of the fall--off in mean energy to
either side of this peak are explained in terms of the occurence of stable,
$\epsilon$--classical dynamics [S. Wimberger, I. Guarneri, and S. Fishman,
\textit{Nonlin.} \textbf{16}, 1381 (2003)] around each quantum resonance.
