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Recurrence rates for loosely Markov dynamical systems

Part of: Complex dynamical systems Smooth dynamical systems: general theory Ergodic theory

Published online by Cambridge University Press:  09 April 2009

Mariusz Urbański
Mariusz Urbański
Affiliation:
Department of MathematicsUniversity of North TexasP.O. Box 311430 Denton TX 76203-1430USA e-mail: [email protected]
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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.

MSC classification

Secondary: 37C45: Dimension theory of dynamical systems 37C40: Smooth ergodic theory, invariant measures 37F35: Conformal densities and Hausdorff dimension 37A25: Ergodicity, mixing, rates of mixing
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 1 , February 2007 , pp. 39 - 57
Copyright
Copyright © Australian Mathematical Society 2007

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