Li–Yorke and Devaney chaotic uniform dynamical systems amongst weighted shifts

Li–Yorke and Devaney chaotic uniform dynamical systems amongst weighted shifts

In this paper, for finite discrete field F, a self–map φ of a nonempty set Γ, weight vector w=(wα)α∈Γ∈FΓ and weighted generalized shift σφ,w:FΓ→FΓ, we introduce necessary and sufficient conditions for uniform dynamical system (FΓ,σφ,w) to be Li–Yorke chaotic. Next we give necessary and sufficient co...

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Veröffentlicht in:Topology and its applications 2023-03, Vol.326, p.108406, Article 108406
Hauptverfasser: Ayatollah Zadeh Shirazi, Fatemah, Hakimi, Elaheh, Hosseini, Arezoo, Rezavand, Reza
Format: Artikel
Sprache:eng
Schlagworte:
Devaney chaotic
Li–Yorke chaotic
Sensitive
Topological transitive
Weighted generalized shift
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Zusammenfassung:In this paper, for finite discrete field F, a self–map φ of a nonempty set Γ, weight vector w=(wα)α∈Γ∈FΓ and weighted generalized shift σφ,w:FΓ→FΓ, we introduce necessary and sufficient conditions for uniform dynamical system (FΓ,σφ,w) to be Li–Yorke chaotic. Next we give necessary and sufficient conditions for (FΓ,σφ,w) to be Devaney chaotic.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2022.108406