Dynamical invariants for group automorphisms

TL;DR

This paper explores the classification of automorphisms of compact abelian groups, especially one-dimensional solenoids, by analyzing dynamical invariants and discussing related open problems.

Contribution

It provides a complete description of automorphisms of one-dimensional solenoids and discusses the range of invariants for topological conjugacy, including new results and open problems.

Findings

Complete classification of automorphisms of one-dimensional solenoids.

Analysis of invariants for topological conjugacy.

Identification of open problems in the classification of group automorphisms.

Abstract

We discuss some of the issues that arise in attempts to classify automorphisms of compact abelian groups from a dynamical point of view. In the particular case of automorphisms of one-dimensional solenoids, a complete description is given and the problem of determining the range of certain invariants of topological conjugacy is discussed. Several new results and old and new open problems are described.