Global Rigidity of Higher Rank Anosov Actions on Tori and Nilmanifolds

TL;DR

This paper proves that certain complex dynamical systems called higher rank Anosov actions on tori and nilmanifolds are essentially equivalent to simpler affine actions through smooth conjugacy.

Contribution

It establishes the smooth conjugacy of sufficiently irreducible higher rank Anosov actions to affine actions on tori and nilmanifolds, advancing understanding of their rigidity.

Findings

Anosov actions are smoothly conjugate to affine actions

Higher rank abelian groups exhibit rigidity in these systems

Results apply to tori and nilmanifolds

Abstract

We show that sufficiently irreducible Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.