Li-Yorke and Devaney chaotic uniform dynamical systems amongst weighted shifts
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913199145615360 |
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| author | Shirazi, Fatemah Ayatollah Zadeh Hakimi, Elaheh Hosseini, Arezoo Rezavand, Reza |
| author_facet | Shirazi, Fatemah Ayatollah Zadeh Hakimi, Elaheh Hosseini, Arezoo Rezavand, Reza |
| contents | In this paper, for finite discrete field $F$, nonempty set $Γ$, weight vector $\mathfrak{w}=({\mathfrak w}_α)_{α\inΓ}\in F^Γ$ and weighted generalized shift $σ_{φ,{\mathfrak w}}:F^Γ\to F^Γ$, we find necessary and sufficient conditions for uniform dynamical system $(F^Γ,σ_{φ,{\mathfrak w}})$ to be Li--Yorke chaotic. Next we find necessary and sufficient conditions for $(F^Γ,σ_{φ,{\mathfrak w}})$ to be Devaney chaotic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2204_07950 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Li-Yorke and Devaney chaotic uniform dynamical systems amongst weighted shifts Shirazi, Fatemah Ayatollah Zadeh Hakimi, Elaheh Hosseini, Arezoo Rezavand, Reza Dynamical Systems 37B02, 54H15 In this paper, for finite discrete field $F$, nonempty set $Γ$, weight vector $\mathfrak{w}=({\mathfrak w}_α)_{α\inΓ}\in F^Γ$ and weighted generalized shift $σ_{φ,{\mathfrak w}}:F^Γ\to F^Γ$, we find necessary and sufficient conditions for uniform dynamical system $(F^Γ,σ_{φ,{\mathfrak w}})$ to be Li--Yorke chaotic. Next we find necessary and sufficient conditions for $(F^Γ,σ_{φ,{\mathfrak w}})$ to be Devaney chaotic. |
| title | Li-Yorke and Devaney chaotic uniform dynamical systems amongst weighted shifts |
| topic | Dynamical Systems 37B02, 54H15 |
| url | https://arxiv.org/abs/2204.07950 |