Open Access
Research Article
Distributional Chaotic Generalized Shifts
*Zahra Nili AhmadabadiCorresponding authorzahra.nili@srbiau.ac.irScience and Research BranchIslamic Azad UniversityTehran, IranView full profile → , Fatemah Ayatollah Zadeh Shirazifatemah@khayam.ut.ac.irFaculty of MathematicsStatistics and Computer Science, College of ScienceUniversity of TehranEnghelab Ave, Tehran, Iran,View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 15 Jan 2019
- Accepted:
- 28 Nov 2019
- Published Online:
- 29 Jul 2020
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- 1726037X.2020.1774156
- Pages:
- 53–70
Abstract
Suppose X is a finite discrete space with at least two elements, Γ is a nonempty countable set, and consider self–map φ: Γ → Γ. We prove that the generalized shift σφ : XΓ→XΓ with σφ((Xα)undefined∈Γ) = (X( (for (X)undefined∈Γ ∈ XΓ) is: distributional chaotic (uniform, type 1, type 2) if and only if φ : Γ → Γ has at least a non-quasi-periodic point, dense distributional chaotic if and only if φ : Γ → Γ does not have any periodic point, transitive distributional chaotic if and only if φ : Γ → Γ is one–to–one without any periodic point. We complete the text by counterexamples.
Keywords
Subject Classifications
54H20
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