Countable Compacta Admitting Homeomorphisms with Positive Sequence Entropy

Let (X, T) be a topological dynamical system (TDS), Ω(T) be the set of non-wondering points and be the topological sequence entropy. In this paper, an example on a countable compactum X with is given. Then for TDSs on countable compacta X, it is proved that when d(X) ≤ 1, ; and when d(X) ≥ 2, there exists a homeomorphism T on X such that X ^d is the sequence entropy set of (X, T), where d(X) and X ^d are the derived degree of X and the set of all accumulation points of X respectively. Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday