  We discuss one parameter families of unimodal maps, with negative Schwarzian
derivative, unfolding a saddle-node bifurcation. It was previously shown that
for a parameter set of positive Lebesgue density at the bifurcation, the maps
possess attracting periodic orbits of high period. We show that there is also a
parameter set of positive density at the bifurcation, for which the maps
exhibit absolutely continuous invariant measures which are supported on the
largest possible interval. We prove that these measures converge weakly to an
atomic measure supported on the orbit of the saddle-node point. Using these
measures we analyze the intermittent time series that result from the
destruction of the periodic attractor in the saddle-node bifurcation and prove
asymptotic formulae for the frequency with which orbits visit the region
previously occupied by the periodic attractor.
