Stable sets and mean Li-Yorke chaos in positive entropy actions of bi-orderable amenable groups

TL;DR

This paper demonstrates that positive entropy in actions of bi-orderable amenable groups leads to mean Li-Yorke chaos, with examples including integer lattice groups and unipotent upper triangular matrices.

Contribution

It establishes a link between positive entropy and mean Li-Yorke chaos for a broad class of group actions, extending previous results to bi-orderable amenable groups.

Findings

Positive entropy implies mean Li-Yorke chaos in these systems.

Examples include actions of integer lattice groups.

Examples also include groups of unipotent upper triangular matrices.

Abstract

It is proved that positive entropy implies mean Li-Yorke chaos for a G-system, where G is a countable infinite discrete bi-orderable amenable group. Examples are given for the cases of integer lattice groups and groups of integer unipotent upper triangular matrices.