On structure of topological entropy for tree-shift of finite type.

This paper deals with the topological entropy for hom Markov shifts T M on d -tree. If M is a reducible adjacency matrix with q irreducible components M 1 , ⋯ , M q , we show that h (T M) = max 1 ≤ i ≤ q ⁡ h (T M i ) fails generally, and present a case study with full characterization in terms of the equality. Though that it is likely the sets { h (T M) : M is binary and irreducible } and { h (T X) : X is a one-sided shift } are not coincident, we show the two sets share the common closure. Despite the fact that such closure is proved to contain the interval [ d log ⁡ 2 , ∞) , numerical experiments suggest its complement contain open intervals. [ABSTRACT FROM AUTHOR]