English

Substitution Dynamical Systems: Characterization of Linear Repetitivity and Applications

Dynamical Systems 2015-02-24 v2 Mathematical Physics math.MP

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 Schr\"odinger operators and to number theory.

Keywords

Cite

@article{arxiv.math/0302231,
  title  = {Substitution Dynamical Systems: Characterization of Linear Repetitivity and Applications},
  author = {D. Damanik and D. Lenz},
  journal= {arXiv preprint arXiv:math/0302231},
  year   = {2015}
}

Comments

14 pages, assumption (4) included

R2 v1 2026-07-22T16:52:08.555Z