Another invariant for AT actions

TL;DR

This paper introduces new numerical invariants for approximately transitive actions of the integers, aiding in distinguishing non-isomorphic actions within certain families.

Contribution

The authors develop a set of invariants for AT actions and demonstrate their effectiveness in classifying actions up to isomorphism.

Findings

Invariants successfully differentiate non-isomorphic AT actions.

Application of invariants to specific one-parameter families.

Enhanced understanding of the structure of AT actions.

Abstract

We construct a collection of numerical invariants for approximately transitive (AT) actions (of $\Z$). We use them (sometimes supplemented by other invariants to show that members of various one-parameter families of AT actions are mutually non-isomorphic.