Quadratic rational maps with a $2$-cycle of Siegel disks
Dynamical Systems
2022-06-30 v2 Complex Variables
Abstract
For the family of quadratic rational functions having a -cycle of bounded type Siegel disks, we prove that each of the boundaries of these Siegel disks contains at most one critical point. In the parameter plane, we prove that the locus for which the boundaries of the -cycle of Siegel disks contain two critical points is a Jordan curve.
Cite
@article{arxiv.2012.10818,
title = {Quadratic rational maps with a $2$-cycle of Siegel disks},
author = {Yuming Fu and Fei Yang and Gaofei Zhang},
journal= {arXiv preprint arXiv:2012.10818},
year = {2022}
}
Comments
21 pages, 7 figures; to appear in the Journal of Geometric Analysis