Sequence entropy for amenable group actions

TL;DR

This paper explores the use of sequence entropy to analyze amenable group actions, providing new insights into spectrum, mixing properties, and characterizations of weakly mixing and null systems in dynamical systems.

Contribution

It introduces systematic methods for studying spectrum and mixing via sequence entropy and characterizes weakly mixing and null systems using sequence entropy pairs.

Findings

Sequence entropy helps classify mixing properties.

Weakly mixing systems characterized by sequence entropy pairs.

New connections between sequence entropy and system nullity.

Abstract

We study the sequence entropy for amenable group actions and investigate systematically spectrum and several mixing concepts via sequence entropy both in measure-theoretic dynamical systems and topological dynamical systems. Moreover, we use sequence entropy pairs to characterize weakly mixing and null systems.