Any counterexample to Makienkos conjecture is an indecomposable continuum

Academic Article

Abstract

  • Makienkos conjecture, a proposed addition to Sullivans dictionary, can be stated as follows: the Julia set of a rational function R: has buried points if and only if no component of the Fatou set is completely invariant under the second iterate of R. We prove Makienkos conjecture for rational functions with Julia sets that are decomposable continua. This is a very broad collection of Julia sets; it is not known if there exists a rational function whose Julia set is an indecomposable continuum. © 2009 Cambridge University Press.
  • Authors

    Published In

    Digital Object Identifier (doi)

    Author List

  • Curry CP; Mayer JC; Meddaugh J; Rogers JT
  • Start Page

  • 875
  • End Page

  • 883
  • Volume

  • 29
  • Issue

  • 3