Self-similar Cut-and-project Sequences

摘要

We consider one-dimensional aperiodic sequences E arising from a two-dimensional cut-and-project scheme. Such sequences are given by two irrational numbers η, ε and by a bounded interval Ω. We give a necessary and sufficient condition on the parameters η, ε and Ω under which Σ is selfsimilar, i.e. there exists a real number γ > 1 such that γΣ is contained in Σ.