Shapes of Polynomial Julia Sets

Abstract

Any Jordan curve in the complex plane can be approximated arbitrarily well in the Hausdorff topology by Julia sets of polynomials. Finite collections of disjoint Jordan domains can be approximated by the basins of attraction of rational maps.

13 pages, 3 figures

Cited by in corpus (5)

• True trees are dense
• On Dynamics of Asymptotically Minimal Polynomials
• On Lagrange polynomials and the rate of approximation of planar sets by polynomial Julia sets
• Attractor sets and Julia sets in low dimensions
• Julia sets of Orthogonal polynomials