Geometrical and spectral properties of Pisot substitutions

摘要

A necessary condition for an n-dimensional substitutive dynamical system to be a finite extension of an algebraic system is that the substitution be Pisot. We discuss the sufficiency of the Pisot property and review conditions under which such an extension is guaranteed to be almost everywhere one-to-one. (C) 2016 Elsevier B.V. All rights reserved.