Models for spaces of dendritic polynomials

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.