An algebraic characterization of expanding Thurston maps
Peter Haïssinsky Kevin M. Pilgrim
Journal of Modern Dynamics 2012, 6(4): 451-476 doi: 10.3934/jmd.2012.6.451
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 $g$.
keywords: expanding. Thurston map virtual endomorphism
Examples of coarse expanding conformal maps
Peter Haïssinsky Kevin M. Pilgrim
Discrete & Continuous Dynamical Systems - A 2012, 32(7): 2403-2416 doi: 10.3934/dcds.2012.32.2403
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.
keywords: conformal dynamics. conformal dimension Menger compacta Iterated function system Thurston obstruction

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