Conjugacy of unimodular pisot substitutions subshifts to domain exchanges
arXiv:1408.2110
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.
arXiv comment30p. Modifications after referee's comments