No or infinitely many ACIP for piecewise expanding C-r maps in higher dimensions

We modify Tsujii's example [9] to show that in contrast with the one-dimens ional. case, piecewise uniformly expanding and C-r maps of the plane may: (1) either have no absolutely continuous invariant probability measures (a. c.i.p. for short) and be such that every point is statistically attracted t o a fixed repelling point; (2) or have infinitely many ergodic a.c.i.p.