J. Buzzi
No or infinitely many a.c.i.p. for piecewise expanding C^r maps in higher dimensions
(215K, postscript)
ABSTRACT. On the interval, any piecewise expanding map which is a little more than C^1 has a finite, noin-zero number of ergodic absolutely continuous invariant probability measures (acip). In higher dimension this is no longer true, even assuming C^r smoothness with arbitrarily large r. We show that there are examples with no acip, and others with infinitely many acip. We build on a previous example of M. Tsujii.