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Recurrence rates for loosely Markov dynamical systems

Published online by Cambridge University Press:  09 April 2009

Mariusz Urbański
Affiliation:
Department of MathematicsUniversity of North TexasP.O. Box 311430 Denton TX 76203-1430USA e-mail: urbanski@unt.edu
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

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