Examples of coarse expanding conformal maps

Peter Haïssinsky; Kevin M. Pilgrim

doi:10.3934/dcds.2012.32.2403

Article Contents

2012, Volume 32, Issue 7: 2403-2416. Doi: 10.3934/dcds.2012.32.2403

This issue Previous Article Measure rigidity for some transcendental meromorphic functions Next Article Continued fractions, Cantor sets, Hausdorff dimension, and transfer operators and their analytic extension

Examples of coarse expanding conformal maps

Peter Haïssinsky^1, and
Kevin M. Pilgrim^2,

1.
Centre de Mathmatiques et Informatique (CMI) et LATP, Aix-Marseille Université, 39, rue F. Joliot Curie 13453 Marseille Cedex 13
2.
Dept. Mathematics, Indiana University, Bloomington, IN 47405

Received: January 31, 2010

Revised: September 30, 2010

Published: June 2012

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Abstract

In previous work, a class of noninvertible topological dynamical systems $f: X \to X$ was introduced and studied; we called these topologically coarse expanding conformal systems. To such a system is naturally associated a preferred quasisymmetry (indeed, snowflake) class of metrics in which arbitrary iterates distort roundness and ratios of diameters by controlled amounts; we called this metrically coarse expanding conformal. In this note we extend the class of examples to several more familiar settings, give applications of our general methods, and discuss implications for the computation of conformal dimension.

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Mathematics Subject Classification: Primary: 30L10, 37F20; Secondary: 28A80.

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