Cubic polynomials with a 2-cycle of Siegel disks
Dynamical Systems
2024-10-23 v1 Complex Variables
Abstract
Under conjugation by affine transformations, the dynamical moduli space of cubic polynomials with a -cycle of Siegel disks is parameterized by a three-punctured complex plane as a degree- cover. Assuming the rotation number of on the Siegel disk is of bounded type, we show that on the three-punctured complex plane, the locus of the cubic polynomials with both finite critical points on the boundaries of the Siegel disks on the -cycle is comprised of two arcs, corresponding to the cases with two critical points on the boundary of the same Siegel disk, and a Jordan curve, corresponding to the cases with two critical points on the boundaries of different Siegel disks.
Keywords
Cite
@article{arxiv.2410.16728,
title = {Cubic polynomials with a 2-cycle of Siegel disks},
author = {Yuming Fu and Jun Hu and Oleg Muzician},
journal= {arXiv preprint arXiv:2410.16728},
year = {2024}
}