2018/08/17 by D. M. Rust, Rust, Dan
Computer Science · Materials Science · #37A50 #37B10 #37B40 #52C23 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Quasicrystal Structures and Properties #semigroups and automata theory
paper · doi:10.48550/arxiv.1808.05934
openalex publication_date 2018/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study various aspects of periodic points for random substitution subshifts. In order to do so, we introduce a new property for random substitutions called the disjoint images condition. We provide a procedure for determining the property for compatible random substitutions-random substitutions for which a well-defined abelianisation exists. We find some simple necessary criteria for primitive, compatible random substitutions to admit periodic points in their subshifts. In the case that the random substitution further has disjoint images and is of constant length, we provide a stronger criterion. A method is outlined for enumerating periodic points of any specified length in a random substitution subshift.