Bounded geometry of quadrilaterals and variation of multipliers for rational maps
Volume 182 / 2004
Fundamenta Mathematicae 182 (2004), 137-150
MSC: Primary 37F30; Secondary 37F10, 30F60.
DOI: 10.4064/fm182-2-4
Abstract
Let $Q$ be the unit square in the plane and $h: Q \to h(Q)$ a quasiconformal map. When $h$ is conformal off a certain self-similar set, the modulus of $h(Q)$ is bounded independent of $h$. We apply this observation to give explicit estimates for the variation of multipliers of repelling fixed points under a “spinning” quasiconformal deformation of a particular cubic polynomial.
