Quadratic-Like Dynamics of Cubic Polynomials

Academic Article

Abstract

  • © 2016, Springer-Verlag Berlin Heidelberg. A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.
  • Digital Object Identifier (doi)

    Author List

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

  • 733
  • End Page

  • 749
  • Volume

  • 341
  • Issue

  • 3