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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.

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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