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   USA   urbanski@unt.edu

Abstract

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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