  We consider the dynamics of a single atom submitted to periodic pulses of a
far-detuned standing wave generated by a high-finesse optical cavity, which is
an atomic version of the well-known ``kicked rotor''. We show that the
classical phase-space map can be ``reconstructed'' by monitoring the
transmission of the cavity. We also studied the effect of spontaneous emission
on the reconstruction, and put limits to the maximum acceptable spontaneous
emission rate.
