  In this paper we characterize $\w$-limit sets of dendritic Julia sets for
quadratic maps. We use Baldwin's symbolic representation of these spaces as a
non-Hausdorff itinerary space and prove that quadratic maps with dendritic
Julia sets have shadowing, and also that for all such maps, a closed invariant
set is an $\w$-limit set of a point if, and only if, it is internally chain
transitive.
