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arXiv · 1408.2110

Conjugacy of unimodular pisot substitutions subshifts to domain exchanges

Samuel Petite·Fabien Durand
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Abstract

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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Samuel Petite, Fabien Durand. 2014-08-09. Conjugacy of unimodular pisot substitutions subshifts to domain exchanges. https://arxiv.org/abs/1408.2110

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