Models for spaces of dendritic polynomials
Dynamical Systems
2021-12-21 v3
Abstract
Complex 1-variable polynomials with connected Julia sets and only repelling periodic points are called \emph{dendritic}. By results of Kiwi, any dendritic polynomial is semi-conjugate to a topological polynomial whose topological Julia set is a dendrite. We construct a continuous map of the space of all cubic dendritic polynomials onto a laminational model that is a quotient space of a subset of the closed bidisk. This construction generalizes the "pinched disk" model of the Mandelbrot set due to Douady and Thurston. It can be viewed as a step towards constructing a model of the cubic connectedness locus.
Keywords
Cite
@article{arxiv.1701.08825,
title = {Models for spaces of dendritic polynomials},
author = {Alexander Blokh and Lex Oversteegen and Ross Ptacek and Vladlen Timorin},
journal= {arXiv preprint arXiv:1701.08825},
year = {2021}
}
Comments
23 pages, 1 figure; in this version the proof of a key lemma was shortened; to appear in Trans. Amer. Math. Soc