Bifurcation from stable fixed point to two-dimensional attractor in the border collision normal form

The border collision normal form is a family of continuous two-dimensional piecewise smooth maps describing dynamics close to a critical parameter at which a fixed point intersects the switching surface. It is well known that if the fixed point is stable on one side of the bifurcation point then after the bifurcation the system may have stable periodic orbits and/or chaotic attractors with a quasi-one dimensional structure (robust chaos). We show that it is also possible to have a robust transition from a stable fixed point to an attractor with topological dimension two, i.e. the highest dimension possible in the phase spac