UNIMODULAR PISOT SUBSTITUTIONS AND DOMAIN EXCHANGES

Fabien Durand (1) , Samuel Petite (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

We show that any Pisot substitution on a finite alphabet is conjugate to a primitive proper substitution (satisfying then a coincidence condition) whose incidence matrix has the same eigenvalues as the original one, with possibly 0 and 1. Then, we prove also substitutive systems sharing this property and admitting "enough" multiplicatively independent eigenvalues (like for unimodular Pisot substitutions) are measurably conjugate to domain exchanges in Euclidean spaces which factorize onto minimal translations on tori. The combination of these results generalizes a well-known result of Arnoux-Ito to any unimodular Pisot substitution.

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

Domaines: Systèmes dynamiques [math.DS]

Fabien Durand, Samuel Petite. UNIMODULAR PISOT SUBSTITUTIONS AND DOMAIN EXCHANGES. 2014. ⟨hal-01053723v1⟩