Rigidity properties for commuting automorphisms on tori and solenoids

TL;DR

This paper proves a measure rigidity theorem for higher rank commuting automorphisms on tori and solenoids with positive entropy, and classifies their disjointness and factors.

Contribution

It introduces a measure rigidity result for higher rank automorphisms and provides a complete classification of disjointness and measurable factors.

Findings

Measure rigidity theorem established for higher rank actions with positive entropy

Complete classification of disjointness for these actions

Characterization of measurable factors for automorphisms on tori and solenoids

Abstract

Assuming positive entropy we prove a measure rigidity theorem for higher rank actions on tori and solenoids by commuting automorphisms. We also apply this result to obtain a complete classification of disjointness and measurable factors for these actions.