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## Models for spaces of dendritic polynomials

Transactions of the American Mathematical Society. 2019. Vol. 372. No. 7. P. 4829-4849.
Alexander B., Lex O., Ptacek R. M., Timorin V.

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.