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Victor Jiménez López; Jose Salvador Cánovas Peña
Computing explicitly topological sequence entropy: the unimodal case
(Calcul explicite de l'entropie topologique séquentielle; le cas unimodal)
Annales de l'institut Fourier, 52 no. 4 (2002), p. 1093-1133, doi: 10.5802/aif.1913
Article PDF | Reviews MR 1926675 | Zbl 1083.37012
Class. Math.: 37B40, 26A18, 54H20
Keywords: map of type $2^\infty$, topological sequence entropy, unimodal map

Résumé - Abstract

Let $W(I)$ denote the family of continuous maps $f$ from an interval $I=[a,b]$ into itself such that (1) $f(a)=f(b)\in\{a,b\}$; (2) they consist of two monotone pieces; and (3) they have periodic points of periods exactly all powers of $2$. The main aim of this paper is to compute explicitly the topological sequence entropy $h_D(f)$ of any map $f\in W(I)$ respect to the sequence $D=(2^{m-1})_{m=1}^\infty$.

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