Normal forms of border collisions in high-dimensional nonsmooth maps

This paper is concerned with the derivation of normal form maps associated to border-collision events in n-dimensional piecewise smooth discrete systems. It is shown that these maps can be put in a standard form by means of appropriate coordinate transformations which reduces, in the two-dimensional case, to the border-collision normal form map studied by Yorke et al. (1994). This represents a key step towards the derivation of a general classification of border-collisions in high-dimensional systems.