The strip entropy approximation of Markov shifts on trees

TL;DR

This paper investigates the strip entropy approximation for Markov shifts on trees, extending previous results to golden-mean trees and certain Markov-Cayley trees, demonstrating its validity in these contexts.

Contribution

It extends the validity of strip entropy approximation from 2-trees to golden-mean trees and specific Markov-Cayley trees, broadening its applicability.

Findings

Strip entropy approximation holds for every ray of a golden-mean tree.

The approximation is valid for eventually periodic rays of certain Markov-Cayley trees.

Results extend previous work on conventional 2-trees.

Abstract

The strip entropy is studied in this article. We prove that the strip entropy approximation is valid for every ray of a golden-mean tree. This result extends the previous result of [Petersen-Salama, Discrete \& Continuous Dynamical Systems, 2020] on the conventional 2-tree. Lastly, we prove that the strip entropy approximation is valid for eventually periodic rays of a class of Markov-Cayley trees.