CONJUGACY OF UNIMODULAR PISOT SUBSTITUTIONS SUBSHIFTS TO DOMAIN EXCHANGES
Résumé
We prove that any unimodular Pisot substitution subshift is measurably conjugate to a domain exchange in an Euclidean space which is a finite topological extension of a translation on a torus.
This generalizes the pioneer works of Rauzy and Arnoux-Ito providing geometric realizations to any unimodular Pisot substitution without any additional combinatorial condition.
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