  We investigate high-order harmonic generation in inhomogeneous media for
reduced dimensionality models. We perform a phase-space analysis, in which we
identify specific features caused by the field inhomogeneity. We compute
high-order harmonic spectra using the numerical solution of the time-dependent
Schr\"odinger equation, and provide an interpretation in terms of classical
electron trajectories. We show that the dynamics of the system can be described
by the interplay of high-frequency and slow-frequency oscillations, which are
given by Mathieu's equations. The latter oscillations lead to an increase in
the cutoff energy, and, for small values of the inhomogeneity parameter, take
place over many driving-field cycles. In this case, the two processes can be
decoupled and the oscillations can be described analytically.
