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 \((G_n)_{n\ge 1}\) ${(G_n)}_{n\ge 1}$ consisting of non-empty finite subsets of G with \(\lim _{n\rightarrow \infty }|G_n|=\infty \) ${lim}_{n\to \infty }|G_n|=\infty$ , Pinsker \(\sigma \) $\sigma$ -algebra is a characteristic factor for \((G_n)_{n\ge 1}\) ${(G_n)}_{n\ge 1}$ . As a consequence, for a class of 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.