Topological sequence entropy of interval maps

Abstract

We establish a full classification of chaotic and non-chaotic interval maps from the point of view of topological sequence entropy. This completes the papers of Franzová and Smítal (1991 Positive sequence topological entropy characterizes chaotic maps Proc. Am. Math. Soc. 112 1083–6) and Hric (1999 Topological sequence entropy for maps of the interval Proc. Am. Math. Soc. 127 2045–52). Moreover, with reference to interval maps, this paper establishes an analogous result to Pickel's result on metric sequence entropy (1969 Some properties of A-entropy Mat. Zametki 5 327–34 (in Russian)), and partially solves a question of Goodman (1974 Topological sequence entropy Proc. Lond. Math. Soc. 29 331–50).