When is the beginning the end? On full trajectories, limit sets and internal chain transitivity

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Abstract

Let f : X → X be a continuous map on a compact metric space X and let αf , ωf and ICTf denote the set of α-limit sets, ω-limit sets and nonempty closed internally chain transitive sets respectively. In this paper we characterise, by introducing novel variants of shadowing, maps for which every element of ICTf is equal to (resp. may be approximated by) the α-limit set and the ω-limit set of the same full trajectory. We construct examples highlighting the difference between these properties.
Original languageEnglish
Article number107934
JournalTopology and its Applications
Volume306
Early online date7 Dec 2021
DOIs
Publication statusPublished - 1 Feb 2022

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