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

The N-dimensional border collision normal form describes bifurcations of piecewise smooth systems. It is shown that there is an open set of parameters such that on one side of the bifurcation the map has a stable fixed point and on the other an attractor with Hausdorff dimension N. For generic parameters this attractor contains open sets and hence has topological dimension equal to N.