Tree shift topological entropy

TL;DR

This paper introduces a new definition of topological entropy for tree shifts, proves its well-definedness, and compares it to the entropy of related one-dimensional shifts, highlighting its theoretical significance.

Contribution

It provides the first formal definition of topological entropy for tree shifts and establishes its relationship with one-dimensional shift entropy.

Findings

The limit defining tree shift entropy exists.

Tree shift entropy bounds the entropy of associated one-dimensional shifts.

The paper clarifies the theoretical properties of entropy in tree shift systems.

Abstract

We give a definition of topological entropy for tree shifts, prove that the limit in the definition exists, and show that it dominates the topological entropy of the associated one-dimensional shift of finite type when the labeling of the tree shares the same restrictions.