Slices of Parameter Space of Cubic Polynomials

Academic Article

Abstract

  • In this paper, we study slices of the parameter space of cubic polynomials, up to affine conjugacy, given by a fixed value of the multiplier at a non-repelling fixed point. In particular, we study the location of the $main\, cubioid$ in this parameter space. The $main\, cubioid$ is the set of affine conjugacy classes of complex cubic polynomials that have certain dynamical properties generalizing those of polynomials $z^2+c$ for $c$ in the filled main cardioid.
  • Keywords

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

  • Blokh A; Oversteegen L; Timorin V