  Makienko's conjecture, a proposed addition to Sullivan's 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 Makienko's 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 functions whose Julia
set is an indecomposable continuum.
