  We generalize the two dimensional Lozi map in order to systematically obtain
piece-wise continuous maps in three and higher dimensions. Similar to
higher-dimensional generalizations of the related Henon map, these
higher-dimensional Lozi maps support hyperchaotic dynamics. We carry out a
bifurcation analysis and investigate the dynamics through both numerical and
analytical means. The analysis is extended to a sequence of approximations that
smooth the discontinuity in the Lozi map.
