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.
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