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

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.