Joinings of three-interval exchange transformations

Abstract

We show that among three-interval exchange transformations there exists a dichotomy: T has minimal self-joinings whenever the associated subshift is linearly recurrent, and is rigid otherwise. We also build a family of simple rigid three-interval exchange transformations, which is a step towards an old question of Veech, and a family of rigid three-interval exchange transformations, which includes Katok's rank-one map.