Irreducible Julia sets of rational functions

Abstract

We prove that a polynomial Julia set which is a finitely irreducible continuum is either an arc or an indecomposable continuum. For the more general case of rational functions, we give a topological model for the dynamics when the Julia set is an irreducible continuum and all indecomposable subcontinua have empty interior.

8 pages, 2 figures

References in corpus (2)

• Locally connected models for Julia sets
• Any counterexample to Makienko's conjecture is an indecomposable continuum