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

Abstract

Abstract In this article, an analogue $h^S_{\rm top}$ of topological sequence entropy is defined for Markov hom tree-shifts. We explore various aspects of $h^S_{\rm top}$, including the existence of the limit in the definition, its relationship to topological entropy, a full characterization of null systems (with zero $h^S_{\rm top}$ for any $S$), and the upper bound as well as denseness of all possible values. The relationship between this quantity and a variant called induced entropy is also breifly discussed