  The border-collision normal form is a canonical form for two-dimensional,
continuous maps comprised of two affine pieces. In this paper we provide a
guide to the dynamics of this family of maps in the non-invertible case where
the two pieces fold onto the same half-plane. We identify parameter regimes for
the occurrence of key bifurcation structures, such as period-incrementing,
period-adding, and robust chaos. We then apply the results to a classic model
of a boost converter for adjusting the voltage of direct current. It is known
that for one combination of circuit parameters the model exhibits a
border-collision bifurcation that mimics supercritical period-doubling and is
non-invertible due to the switching mechanism of the converter. We find that
over a wide range of parameter values, even though the dynamics created in
border-collision bifurcations is in general extremely diverse, the bifurcation
in the boost converter can only mimic period-doubling, although it can be
subcritical.
