Pinsker $\sigma$-algebra Character and mean Li-Yorke chaos

Let $G$ be an infinite countable discrete amenable group. For any $G$-action on a compact metric space $X$, it is proved that for any sequence $(G_n){n\ge 1}$consistingofnon-emptyfinitesubsetsof$G$with$\lim{n\to \infty}|G_n|=\infty$,Pinsker$\sigma$-algebraisacharacteristicfactorfor$(G_n)_{n\ge 1}$\mathrm{.}Asaconsequence,foraclassof$G$-topological dynamical systems, positive topological entropy implies mean Li-Yorke chaos along a class of sequences consisting of non-empty finite subsets of $G$.