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