Abstract:
We modify Tsujii's example [9] to show that in contrast with the one-dimensional 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 {\bf every point} is statistically attracted to a fixed repelling point;¶
(2) or have infinitely many ergodic a.c.i.p.
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Received: 6 September 2000 / Accepted: 15 May 2001
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Buzzi, J. No or Infinitely Many A.C.I.P.¶for Piecewise Expanding Cr Maps¶in Higher Dimensions. Commun. Math. Phys. 222, 495–501 (2001). https://doi.org/10.1007/s002200100509
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DOI: https://doi.org/10.1007/s002200100509