Tree shift topological entropy
Karl Petersen, Ibrahim Salama

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.
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Taxonomy
TopicsCellular Automata and Applications · Mathematical Dynamics and Fractals · semigroups and automata theory
