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Tree-shifts: the entropy of tree-shifts of finite type

2017; IOP Publishing; Volume: 30; Issue: 7 Linguagem: Inglês

10.1088/1361-6544/aa72c0

ISSN

1361-6544

Autores

Jung-Chao Ban, Chih-Hung Chang,

Tópico(s)

Nonlinear Dynamics and Pattern Formation

Resumo

This paper studies the entropy of tree-shifts of finite type with and without boundary conditions. We demonstrate that computing the entropy of a tree-shift of finite type is equivalent to solving a system of nonlinear recurrence equations. Furthermore, the entropy of the binary Markov tree-shifts over two symbols is either 0 or . Meanwhile, the realization of a class of reals including multinacci numbers is elaborated, which indicates that tree-shifts are capable of rich phenomena. By considering the influence of three different types of boundary conditions, say, the periodic, Dirichlet, and Neumann boundary conditions, the necessary and sufficient conditions for the coincidence of entropy with and without boundary conditions are addressed.

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