Topological polynomials with a simple core

Academic Article

Abstract

  • We define the (dynamical) core of a topological polynomial (and the associated lamination). This notion extends that of the core of a unimodal interval map. Two explicit descriptions of the core are given: one related to periodic objects and one related to critical objects. We describe all laminations associated with quadratic and cubic topological polynomials with a simple core (in the quadratic case, these correspond precisely to points on the Main Cardioid of the Mandelbrot set).
  • Keywords

  • math.DS, math.DS, 37F20
  • Author List

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