Periodic points in random substitution subshifts

Rust, Dan (2020). Periodic points in random substitution subshifts. Monatshefte für Mathematik, 193 pp. 683–704.

DOI: https://doi.org/10.1007/s00605-020-01458-9

Abstract

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.

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About

• Item ORO ID
• 71859
• Item Type
• Journal Item
• ISSN
• 0026-9255
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications	CRC 1283	German Research Foundation
  Projekt DEAL	Not Set	Not Set

• Keywords
• Random substitutions; Periodic points; Topological entropy
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2020 The Author(s)
• Depositing User
• Dan Rust