Examples of coarse expanding conformal maps

Peter Haïssinsky (1) , Kevin Pilgrim (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Dept. of Mathematics

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.

Domaines: Systèmes dynamiques [math.DS]

Peter Haïssinsky, Kevin Pilgrim. Examples of coarse expanding conformal maps. Discrete and Continuous Dynamical Systems - Series A, 2012, 32 (no. 7), pp.2403 -- 2416. ⟨hal-00530841⟩