  Heterodimensional cycles are heteroclinic cycles that connect periodic orbits
whose unstable manifolds have different dimensions. This is a source of
nonhyperbolic dynamics and unstable dimension variability. For smooth
invertible maps persistence of heterodimensional cycles with changing
parameters is established using blenders, and this is only possible for systems
of dimension three or higher. Using the idea of a snapback repeller we show
that the definitions and results extend to noninvertible maps and that
blender-type dynamics is possible in two dimensional piecewise smooth
noninvertible maps. These piecewise smooth maps have the additional property of
robust chaos, which simplifies some steps of the argument. The ideas are
illustrated using a class of continuous piecewise smooth maps related to the
border collision normal form.
