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

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