00-253 J. Buzzi
No or infinitely many a.c.i.p. for piecewise expanding C^r maps in higher dimensions (215K, postscript) Jun 1, 00
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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.

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