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

Abstract

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

References in corpus (3)

• Mean Li-Yorke chaos along some good sequences
• Positive entropy implies chaos along any infinite sequence
• Combinatorial independence and naive entropy

Cited by in corpus (1)

• Directional Pinsker algebra and its applications