Journal of the Australian Mathematical Society

Research Article

Recurrence rates for loosely Markov dynamical systems

Mariusz Urbańskia1

a1 Department of Mathematics University of North Texas P.O. Box 311430 Denton TX 76203-1430 USA e-mail:


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.

(Received January 19 2004)

(Revised June 06 2005)

2000 Mathematics subject classification

  • primary 37C45;
  • secondary 37C40;
  • 37F35;
  • 37A25