Computing explicitly topological sequence entropy: the unimodal case

[Calcul explicite de l'entropie topologique séquentielle; le cas unimodal]

Jiménez López, Victor ; Cánovas Peña, Jose Salvador

Annales de l'Institut Fourier, Tome 52 (2002), p. 1093-1133 / Harvested from Numdam

Résumé

Nous considérons $W(I)$ la famille de fonctions $f$ continues de l’intervalle $I=[a,b]$ sur lui–même, telles que (1) $f(a)=f(b)\in \lbrace a,b \rbrace $; (2) elles sont constituées de deux morceaux monotones; et (3) elles ont des points périodiques de périodes toutes les puissances de $2$ exactement. L’objectif principal de ce travail est de calculer explicitement l’entropie topologique séquentielle $h_D(f)$ de tout élément $f$ de $W(I)$ par rapport à la suite $D=(2^{m-1})_{m=1}^{ \infty }$.

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 \lbrace a,b\rbrace $; (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 $.

Détail

Publié le : 2002-01-01

MR 1926675 | Zbl 1083.37012

DOI : https://doi.org/10.5802/aif.1913
Classification:  37B40,  26A18,  54H20
Mots clés: fonction de type $2^\infty $, entropie séquentielle topologique, fonction unimodale

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