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Communications in Mathematical Physics

, Volume 222, Issue 3, pp 495–501 | Cite as

No or Infinitely Many A.C.I.P.¶for Piecewise Expanding Cr Maps¶in Higher Dimensions

  • Jérôme Buzzi

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jérôme Buzzi
    • 1
  1. 1.Centre de Mathématiques de l'Ecole Polytechnique U.M.R. 7640 du C.N.R.S., 91128 Palaiseau Cedex, France. E-mail: buzzi@math.polytechnique.frFR

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