No or Infinitely Many A.C.I.P.¶for Piecewise Expanding Cr Maps¶in Higher Dimensions
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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.
Keywords
Probability Measure High Dimension Invariant Probability Measure Continuous Invariant Probability Measure Repelling Point
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag Berlin Heidelberg 2001