Geodesic
Topological sequence entropy for maps of the circle
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 1, pp. 53-59

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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.
Classification : 26A18, 37B40, 37D45, 37E10, 54H20, 58F13
Keywords: chaotic map; circle map; topological sequence entropy 
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Hric, Roman. Topological sequence entropy for maps of the circle. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 1, pp. 53-59. http://geodesic.mathdoc.fr/item/CMUC_2000__41_1_a4/