INTERVAL EXCHANGE TRANSFORMATION EXTENSION OF A SUBSTITUTION DYNAMICAL SYSTEM

Abstract

Let α be a free group automorphism on FN with maximal index and Σα the associated attracting subshift. We prove that there exists an Interval Exchange Transformation on the circle whose coding factorizes onto Σα. In the case when there is an explicit construction of the ℝ-tree associated to α, we construct algorithmically such IET. We conclude by giving examples.