The omega-limit sets of quadratic Julia sets

2012/05/01 by Andrew Barwell, Barwell, Andrew, Brian Raines +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.1205.0191

24 pages

arxiv created 2012/05/01 · openalex publication_date 2012/05/01 · arxiv updated 2012/05/02 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

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.

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