A Remark on Topological Sequence Entropy

Let h∞(T) be the supremum of all topological sequence entropies of a dynamical system (X,T). This paper obtains the iteration invariance and commutativity of h∞(T) and proves that if T is a multisensitive transformation defined on a locally connected space, then h∞(T) = +∞. As an application, it is shown that a Cournot map is Li–Yorke chaotic if and only if its topological sequence entropy relative to a suitable sequence is positive.