Substitution Dynamical Systems: Characterization of Linear Repetitivity and Applications

Abstract

We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive substitutions to minimal substitutions. This includes applications to random Schrödinger operators and to number theory.

14 pages, assumption (4) included