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arXiv · 2102.07466

Modeling core parts of Zakeri slices I

Alexander Blokh·Lex Oversteegen·Anastasia Shepelevtseva·Vladlen Timorin
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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.

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Alexander Blokh, Lex Oversteegen, Anastasia Shepelevtseva, Vladlen Timorin. 2021-02-15. Modeling core parts of Zakeri slices I. https://arxiv.org/abs/2102.07466

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