On inverse shadowing

Abstract

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Preservation of shadowing in discrete dynamical systems

“…Compact metric versions of the two results below may be found in [21]; the authors remark that the compact metric versions extend to these two results. Lemma 13.0.1.…”

Several generalized K-shadowing properties characteristics in metric space

“…Regarding collection dynamics in a metric space including an applicability to iterated system, bi-shadowing was taken into consideration; view [20]. Diamond et al, [21] were investigated the fatuous homeomorphisms on compact configurations and displayed all inverse shadowing and bishadowing characteristics in relation to a class of techniques that are defined by continuous mappings from exhaust system into the space of bi-infinite sequences in the exhaust system also with product topology [22]. Such systems were shown to demonstrate the idea of bi-shadowing with regard to continuous comparative mappings for these differently under different circumstances.…”

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

“…It has been studied in a variety of settings, including, for example, in the context of Axiom A diffeomorphisms [6], in numerical analysis [13,14,37], as an important factor in stability theory [40,43,47] and as a property in and of itself [15,22,25,30,33,34,38,40,44]. Various variants on the pseudo-orbit tracing property have also been studied including, for example, ergodic, thick, and Ramsey shadowing [7,8,18,19,36], limit, or asymptotic, shadowing [3,26,41], s-limit shadowing [3,26,30], orbital shadowing [21,33,39,41], and inverse shadowing [14,24,29]. In the first stage of this journey, Good and Meddaugh [21] introduced new variants of shadowing which precisely characterise maps for which ω f = ICT f and ω f = ICT f .…”