On the minimal components of substitution subshifts

TL;DR

This paper characterizes the minimal components of substitution subshifts on finite alphabets, providing bounds, descriptions of their dynamics, and an algorithmic method for computation and counting.

Contribution

It offers a precise characterization of minimal components, an optimal bound on their number, and an explicit algorithm for their computation in substitution subshifts.

Findings

Characterization of minimal components in substitution subshifts

Optimal bound for the number of minimal components

Algorithmic method to compute and count minimal components

Abstract

In this paper we study substitutions on $A^\mathbb{Z}$ where $A$ is a finite alphabet. We precisely characterize the minimal components of substitution subshifts, give an optimal bound for their number and describe their dynamics. The explicitness of these results provides a method to algorithmically compute and count the minimal components of a given substitution subshift.