Characterization for entropy of shifts of finite type on Cayley trees

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 $\frac{1}{p}\ln \lambda$ 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.

References in corpus (2)

• Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
• Genericity of dimension drop on self-affine sets

Cited by in corpus (5)

• Mixing properties of tree-shifts
• Coloring Fibonacci-Cayley tree: An application to neural networks
• On the topological entropy of subshifts of finite type on free semigroups
• Complexity of Shift Spaces on Semigroups
• Tree shift topological entropy