Mating Siegel Quadratic Polynomials
Dynamical Systems
2007-05-23 v1
Abstract
Let F be a quadratic rational map of the sphere which has two fixed Siegel disks with bounded type rotation numbers theta and nu. Using a new degree 3 Blaschke product model for the dynamics of F and an adaptation of complex a priori bounds for renormalization of critical circle maps, we prove that F can be realized as the mating of two Siegel quadratic polynomials with the corresponding rotation numbers theta and nu.
Cite
@article{arxiv.math/9808009,
title = {Mating Siegel Quadratic Polynomials},
author = {Michael Yampolsky and Saeed Zakeri},
journal= {arXiv preprint arXiv:math/9808009},
year = {2007}
}
Comments
55 pages, 14 PostScript figures