Shifts of finite type and random substitutions

Gohlke, Philipp; Rust, Dan and Spindeler, Timo (2019). Shifts of finite type and random substitutions. Discrete & Continuous Dynamical Systems - A, 39(9) pp. 5085–5103.

DOI: https://doi.org/10.3934/dcds.2019206

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 the logarithm of 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.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

About

• Item ORO ID
• 70948
• Item Type
• Journal Item
• ISSN
• 1553-5231
• 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	DFG
  Research Centre for Mathematical Modelling	RCM2	Bielefeld University

• Keywords
• Random substitutions; shifts of finite type; 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)
• Depositing User
• Dan Rust