  In diverse physical systems stable oscillatory solutions devolve into more
complicated dynamical behaviour through border-collision bifurcations.
Mathematically these occur when a stable fixed point of a piecewise-smooth map
collides with a switching manifold as parameters are varied. The purpose of
this paper is to highlight the extreme complexity possible in the subsequent
dynamics. We perturb instances of the border-collision normal form in $n \ge 2$
dimensions for which the $n^{\rm th}$ iterate is a direct product of identical
skew tent maps that have chaotic attractors comprised of $k \ge 2$ disjoint
intervals. The resulting maps have coexisting attractors and we use Burnside's
lemma to count the number of mutually disjoint trapping regions produced by
taking unions of Cartesian products of slight enlargements of the disjoint
intervals. The attractors are shown to be chaotic by demonstrating that some
iterate of the map is piecewise-expanding. The resulting transition from a
stable fixed point to many coexisting chaotic attractors is shown to occur
throughout open subsets of parameter space and not destroyed by adding higher
order terms to the normal form, hence can be expected to arise generically in
mathematical models.
