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arXiv · 1705.03138

Characterization for entropy of shifts of finite type on Cayley trees

Jung-Chao Ban·Chih-Hung Chang
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Abstract

The notion of tree-shifts constitutes an intermediate class in between one-sided shift spaces and multidimensional ones. This paper proposes an algorithm for computing of the entropy of a tree-shift of finite type. Meanwhile, the entropy of a tree-shift of finite type is $\dfrac{1}{p} \ln \lambda$ for some $p \in \mathbb{N}$, where $\lambda$ is a Perron number. This extends Lind's work on one-dimensional shifts of finite type. As an application, the entropy minimality problem is investigated, and we obtain the necessary and sufficient condition for a tree-shift of finite type being entropy minimal with some additional conditions.

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Jung-Chao Ban, Chih-Hung Chang. 2017-05-09. Characterization for entropy of shifts of finite type on Cayley trees. https://arxiv.org/abs/1705.03138

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