Two-dimensional attractors in the border-collision normal form

New techniques are developed to show that the two-dimensional normal form for codimension one border-collision bifurcations of fixed points of discrete time piecewise smooth dynamical systems has attractors which are themselves two-dimensional regions with polygonal boundaries. This makes it possible to prove the existence of these attractors for a countable set of parameter values which cannot be treated using the essentially one-dimensional methods in the literature