Characterization and topological behavior of homomorphism tree-shifts

An analogue of topological sequence entropy for Markov hom tree-shifts

“…[20,7]). Its topological behavior and entropy have been extensively studied during the last decade: see [2,3] for the topological behavior, [1] for the classification theory and [4,24,25] for entropy. It is worth noting that since amenability is no longer true for T , that is, |∆ n \∆ n−1 |/|∆ n | does not tend to 0 as n → ∞ (see [7]), where ∆ n denotes the set of all vertices of T whose distance from 0 is at most n, T A has interesting properties which are different from those of shift spaces defined on N or on amenable groups.…”