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arXiv · 2204.07950

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

Fatemah Ayatollah Zadeh Shirazi·Elaheh Hakimi·Arezoo Hosseini·Reza Rezavand
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Abstract

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

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Fatemah Ayatollah Zadeh Shirazi, Elaheh Hakimi, Arezoo Hosseini, Reza Rezavand. 2022-04-17. Li-Yorke and Devaney chaotic uniform dynamical systems amongst weighted shifts. https://arxiv.org/abs/2204.07950

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