Andrew Barwell, Brian Raines
Published 2012-05-01Version 1
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.
Moduli spaces of quadratic maps: arithmetic and geometry
Classification of critical sets and their images for quadratic maps of the plane
Omega-limit sets and invariant chaos in dimension one
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