Shifts of finite type and random substitutions
Dynamical Systems
2020-04-15 v1
Abstract
We prove that every topologically transitive shift of finite type in one dimension is topologically conjugate to a subshift arising from a primitive random substitution on a finite alphabet. As a result, we show that the set of values of topological entropy which can be attained by random substitution subshifts contains all Perron numbers and so is dense in the positive real numbers. We also provide an independent proof of this density statement using elementary methods.
Keywords
Cite
@article{arxiv.1712.05340,
title = {Shifts of finite type and random substitutions},
author = {Philipp Gohlke and Dan Rust and Timo Spindeler},
journal= {arXiv preprint arXiv:1712.05340},
year = {2020}
}