Graph maps with zero topological entropy and sequence entropy pairs

Topological Sequence Entropy and Chaos of Star Maps*

Let Xn = {z ∈ C : z n ∈ [0, 1]}, n ∈ N, and let f : Xn → Xn be a continuous map such that f(0) = 0. In this paper we prove that f is chaotic in the sense of Li–Yorke iff there is a strictly increasing sequence of positive integers A such that the topological sequence entropy of f relative to A is positive.

Topological Sequence Entropy

Statistical Convergent Topological Sequence Entropy Maps of the Circle

A continuous map f of the interval is chaotic iff there is an increasing of nonnegative integers T such that the topological sequence entropy of f relative to T, hT(f), is positive [4]. On the other hand, for any increasing sequence of nonnegative integers T there is a chaotic map f of the interval such that hT(f)=0 [7]. We prove that the same results hold for maps of the circle. We also prove ...

Topological Sequence Entropy for Maps of the Interval

A result by Franzová and Smı́tal shows that a continuous map of the interval into itself is chaotic if and only if its topological sequence entropy relative to a suitable increasing sequence of nonnegative integers is positive. In the present paper we prove that for any increasing sequence of nonnegative integers there exists a chaotic continuous map with zero topological sequence entropy relati...

Topological sequence entropy for maps of the circle

A continuous map f of the interval is chaotic iff there is an increasing sequence of nonnegative integers T such that the topological sequence entropy of f relative to T , hT (f), is positive ([FS]). On the other hand, for any increasing sequence of nonnegative integers T there is a chaotic map f of the interval such that hT (f) = 0 ([H]). We prove that the same results hold for maps of the cir...