Abstract: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 $T$, $h_T(f)$, 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 $h_T(f)=0$ ([H]). We prove that the same results hold for maps of the circle. We also prove some preliminary results concerning topological sequence entropy for maps of general compact metric spaces.
Keywords: chaotic map, circle map, topological sequence entropy
AMS Subject Classification: Primary 26A18, 54H20, 58F13