Topological conjugacy of constant length substitution dynamical systems
Abstract
Primitive constant length substitutions generate minimal symbolic dynamical systems. In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate systems. We show that each conjugacy class contains infinitely substitutions which are not injective. As examples, the Toeplitz conjugacy class contains three injective substitutions (two on two symbols and one on three symbols), and the length two Thue-Morse conjugacy class contains twelve substitutions, among which are two on six symbols. Together, they constitute a list of all primitive substitutions of length two with infinite minimal systems which are factors of the Thue-Morse system.
Keywords
Cite
@article{arxiv.1401.0126,
title = {Topological conjugacy of constant length substitution dynamical systems},
author = {Ethan M. Coven and F. Michel Dekking and Michael S. Keane},
journal= {arXiv preprint arXiv:1401.0126},
year = {2017}
}
Comments
This is version 4, with many improvements over version 3