The omega-limit sets of quadratic Julia sets

Andy D Barwell, Brian Raines

Research output: Contribution to journalArticle (Academic Journal)peer-review

11 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalErgodic Theory and Dynamical Systems
VolumeOnline
Early online date27 Sep 2013
DOIs
Publication statusPublished - 2013

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