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DCDS

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.
JMD

Let $f\colon S^2 \to S^2$ be a postcritically finite branched covering map
without periodic branch points. We give necessary and sufficient
algebraic conditions for $f$ to be homotopic, relative to its
postcritical set, to an expanding map $g$.

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