J. Aust. Math. Soc.  82 (2007), 39-57
Recurrence rates for loosely Markov dynamical systems

Mariusz Urbanski
  Department of Mathematics
  University of North Texas
  P.O. Box 311430
  Denton TX 76203-1430

The concept of loosely Markov dynamical systems is introduced. We show that for these systems the recurrence rates and pointwise dimensions coincide. The systems generated by hyperbolic exponential maps, arbitrary rational functions of the Riemann sphere, and measurable dynamical systems generated by infinite conformal iterated function systems are all checked to be loosely Markov.
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