Furstenberg families and transitivity in non-autonomous systems

TL;DR

This paper establishes conditions for Furstenberg family-based transitivity and mixing in non-autonomous systems, offering characterizations of topological ergodicity and illustrating with examples and counterexamples.

Contribution

It provides necessary and sufficient conditions for Furstenberg family-based properties in non-autonomous systems, advancing understanding of their ergodic behavior.

Findings

Characterization of $$-transitivity and $$-mixing

Conditions for topological ergodicity

Examples and counterexamples illustrating the results

Abstract

We obtain necessary and sufficient conditions for a non-autonomous system to be $\mathcal{F}$-transitive and $\mathcal{F}$-mixing, where $\mathcal{F}$ is a Furstenberg family. We also obtain some characterizations for topologically ergodic non-autonomous systems. We provide examples/counter examples related to our results.