Conjugation between tree-subshifts of finite type and Markov tree-subshifts in examples
DOI:
https://doi.org/10.5902/2179460X90142Keywords:
Trees, Tree-shifts, Conjugation, Dynamical systemsAbstract
Tree-shifts are a class of discrete dynamical systems, from a certain point of view, intermediate between one-dimensional and multidimensional symbolic dynamics. The concept of conjugation between tree-subshifts has great relevance in this context, since it allows different dynamical systems to be related. It is possible, for example, to obtain several properties of a tree-subshift of finite type from the Markov tree-subshift conjugated to it, for which several results can be found in the literature. However, due to the lack of examples that explore such properties, in this work we present two examples of conjugation between a tree-subshift of finite type and a Markov tree-subshift given by transition matrices and obtain descriptions about the value of entropy, irreducibility, mixing, density of periodic points and chaos in the sense of Devaney of the first from the second.
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