Models for spaces of dendritic polynomials

Academic Article

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.
  • Keywords

  • math.DS, math.DS, 37F20 (Primary), 37F10, 37F50 (Secondary)
  • Author List

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