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arXiv · 1701.08825

Models for spaces of dendritic polynomials

Alexander Blokh·Lex Oversteegen·Ross Ptacek·Vladlen Timorin
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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.

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Alexander Blokh, Lex Oversteegen, Ross Ptacek, Vladlen Timorin. 2017-01-30. Models for spaces of dendritic polynomials. https://arxiv.org/abs/1701.08825

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