Weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems

TL;DR

This paper explores the relationships between weakly mixing, topologically weakly mixing, and sensitivity in non-autonomous discrete systems, generalizing known results from autonomous systems and providing counterexamples.

Contribution

It establishes implications among these properties for non-autonomous systems and extends existing autonomous system results with weaker conditions.

Findings

Weakly mixing implies topologically weakly mixing and sensitivity in measurable systems.

Topological weakly mixing implies sensitivity in general systems.

Counterexamples show inverse implications do not hold.

Abstract

This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable systems with a fully supported measure; and topological weakly mixing implies sensitivity for general dynamical systems. However, the inverse conclusions are not true and some counterexamples are given. The related existing results for autonomous discrete systems are generalized to non-autonomous discrete systems and their conditions are weaken.