  We study single-field inflationary models with steep step-like features in
the potential that lead to the temporary violation of the slow-roll conditions
during the evolution of the inflaton. These features enhance the power spectrum
of the curvature perturbations by several orders of magnitude at certain scales
and also produce prominent oscillatory patterns. We study analytically and
numerically the inflationary dynamics. We describe quantitatively the size of
the enhancement, as well as the profile of the oscillations, which are shaped
by the number and position of the features in the potential. The induced tensor
power spectrum inherits the distinctive oscillatory profile of the curvature
spectrum and is potentially detectable by near-future space interferometers.
The enhancement of the power specrtum by step-like features, though
significant, may be insufficient to trigger the production of a sizeable number
of primordial black holes if radiation dominates the energy density of the
early universe. However, it can result in sufficient black hole production if
the universe is dominated by non-relativistic matter. For the latter scenario,
we find that deviations from the standard monochromatic profile of the mass
spectrum of primordial black holes are possible because of the multiple-peak
structure of the curvature power spectrum.
