Modeling core parts of Zakeri slices I
Abstract
The paper deals with cubic 1-variable polynomials whose Julia sets are connected. Fixing a bounded type rotation number, we obtain a slice of such polynomials with the origin being a fixed Siegel point of the specified rotation number. Such slices as parameter spaces were studied by S. Zakeri, so we call them Zakeri slices. We give a model of the central part of a slice (the subset of the slice that can be approximated by hyperbolic polynomials with Jordan curve Julia sets), and a continuous projection from the central part to the model. The projection is defined dynamically and agrees with the dynamical-analytic parameterization of the Principal Hyperbolic Domain by Petersen and Tan Lei.
Keywords
Cite
@article{arxiv.2102.07466,
title = {Modeling core parts of Zakeri slices I},
author = {Alexander Blokh and Lex Oversteegen and Anastasia Shepelevtseva and Vladlen Timorin},
journal= {arXiv preprint arXiv:2102.07466},
year = {2021}
}
Comments
37 pages, 5 figures; to appear in Moscow Math. J. This ver: figures and explanations added