Examples of coarse expanding conformal maps

TL;DR

This paper extends the class of topologically coarse expanding conformal systems to more familiar settings, explores their metric properties, and discusses implications for conformal dimension computation.

Contribution

It broadens the examples of coarse expanding conformal maps, linking abstract theory with concrete settings and applications.

Findings

Extended the class of examples to familiar settings

Provided applications of the general methods

Discussed implications for conformal dimension

Abstract

In previous work, a class of noninvertible topological dynamical systems $f: X \to X$ was introduced and studied; we called these {\em 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 {\em 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.