CONJUGACY OF UNIMODULAR PISOT SUBSTITUTIONS SUBSHIFTS TO DOMAIN EXCHANGES

Samuel Petite (1) , Fabien Durand (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

We prove that any unimodular Pisot substitution subshift is measurably conjugate to a domain exchange in Euclidean spaces which factorizes onto a minimal rotation 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.

Mots clés: substitutions; minimal Cantor systems; eigenvalues; Pisot conjecture

Mots clés: substitutions

Domaines: Systèmes dynamiques [math.DS]

Samuel Petite, Fabien Durand. CONJUGACY OF UNIMODULAR PISOT SUBSTITUTIONS SUBSHIFTS TO DOMAIN EXCHANGES. 2020. ⟨hal-01053723v3⟩