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Interval exchange transformation extension of a substitution dynamical system. (English) Zbl 1353.37025
Summary: Let $$\alpha$$ be a free group automorphism on $$F_N$$ with maximal index and $$\Sigma_{\alpha}$$ the associated attracting subshift. We prove that there exists an Interval Exchange Transformation on the circle whose coding factorizes onto $$\Sigma_\alpha$$. In the case when there is an explicit construction of the $$\mathbb R$$-tree associated to $$\alpha$$, we construct algorithmically such IET. We conclude by giving examples.

##### MSC:
 37B10 Symbolic dynamics 37E05 Dynamical systems involving maps of the interval 37E25 Dynamical systems involving maps of trees and graphs 20E08 Groups acting on trees 20E36 Automorphisms of infinite groups
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