English

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

Dynamical Systems 2024-01-19 v1

Abstract

In this paper, for finite discrete field FF, nonempty set Γ\Gamma, weight vector w=(wα)αΓFΓ\mathfrak{w}=({\mathfrak w}_\alpha)_{\alpha\in\Gamma}\in F^\Gamma and weighted generalized shift σφ,w:FΓFΓ\sigma_{\varphi,{\mathfrak w}}:F^\Gamma\to F^\Gamma, we find necessary and sufficient conditions for uniform dynamical system (FΓ,σφ,w)(F^\Gamma,\sigma_{\varphi,{\mathfrak w}}) to be Li--Yorke chaotic. Next we find necessary and sufficient conditions for (FΓ,σφ,w)(F^\Gamma,\sigma_{\varphi,{\mathfrak w}}) to be Devaney chaotic.

Keywords

Cite

@article{arxiv.2204.07950,
  title  = {Li-Yorke and Devaney chaotic uniform dynamical systems amongst weighted shifts},
  author = {Fatemah Ayatollah Zadeh Shirazi and Elaheh Hakimi and Arezoo Hosseini and Reza Rezavand},
  journal= {arXiv preprint arXiv:2204.07950},
  year   = {2024}
}

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15 pages