Set-theoretical entropies of generalized shifts
In the following text for arbitrary X with at least two elements, nonempty set Γ and self-map φ: Γ → Γ, we prove the set-theoretical entropy of generalized shift σφ: XΓ → XΓ (σφ((xα)α ∈ Γ) = (xφ(α))α ∈ Γ (para (xα)α ∈ Γ ∈ XΓ) is either zero or infinity, moreover it is zero if and only if φ is quasi-...
- Autores:
-
Nili Ahmadabadi, Zahra
Ayatollah Zadeh Shirazi, Fatemah
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2017
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/68371
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/68371
http://bdigital.unal.edu.co/69404/
- Palabra clave:
- 51 Matemáticas / Mathematics
Bounded map
Contravariant set-theoretical entropy
Quasi-periodic
Set-theoretical entropy
función acotada
entropía conjuntista contravariante
casi periodicidad
entropía conjuntista
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | In the following text for arbitrary X with at least two elements, nonempty set Γ and self-map φ: Γ → Γ, we prove the set-theoretical entropy of generalized shift σφ: XΓ → XΓ (σφ((xα)α ∈ Γ) = (xφ(α))α ∈ Γ (para (xα)α ∈ Γ ∈ XΓ) is either zero or infinity, moreover it is zero if and only if φ is quasi-periodic. We continue our study on contravariant set-theoretical entropy of generalized shift and motivate the text using counterexamples dealing with algebraic, topological, set-theoretical and contravariant set-theoretical positive entropies of generalized shifts. |
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