Models for spaces of dendritic polynomials

Academic Article

Abstract

  • © 2019 American Mathematical Society 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.
  • Digital Object Identifier (doi)

    Author List

  • Blokh A; Oversteegen L; Ptacek R; Timorin V
  • Start Page

  • 4829
  • End Page

  • 4849
  • Volume

  • 372