Let Q be the unit square in the plane and h: Q → 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm182-2-4,
author = {Kevin M. Pilgrim},
title = {Bounded geometry of quadrilaterals and variation of multipliers for rational maps},
journal = {Fundamenta Mathematicae},
volume = {184},
year = {2004},
pages = {137-150},
zbl = {1125.37036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm182-2-4}
}
Kevin M. Pilgrim. Bounded geometry of quadrilaterals and variation of multipliers for rational maps. Fundamenta Mathematicae, Tome 184 (2004) pp. 137-150. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm182-2-4/