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

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 00-253.src( 00-253.keywords , modtsj.ps )