Models for spaces of dendritic polynomials

Blokh, Alexander; Oversteegen, Lex; Ptacek, Ross; Timorin, Vladlen

doi:10.1090/tran/7482

Models for spaces of dendritic polynomials
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by Alexander Blokh, Lex Oversteegen, Ross Ptacek and Vladlen Timorin PDF

Trans. Amer. Math. Soc. 372 (2019), 4829-4849 Request permission

Abstract:

Complex 1-variable polynomials with connected Julia sets and only repelling periodic points are called dendritic. By results of Kiwi, any dendritic polynomial is semiconjugate 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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