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 language | English |
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Article number | 107934 |
Journal | Topology and its Applications |
Volume | 306 |
Early online date | 7 Dec 2021 |
DOIs | |
Publication status | Published - 1 Feb 2022 |
Keywords
- Internally chain transitive set
- Pseudo-orbit
- Shadowing
- α-limit set
- ω-limit set
ASJC Scopus subject areas
- Geometry and Topology