Computing explicitly topological sequence entropy: the unimodal case
Annales de l'Institut Fourier, Volume 52 (2002) no. 4, pp. 1093-1133.

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){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 fW(I) respect to the sequence D=(2 m-1 ) m=1 .

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){a,b}; (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 .

DOI: 10.5802/aif.1913
Classification: 37B40,  26A18,  54H20
Keywords: map of type 2 , topological sequence entropy, unimodal map
Jiménez López, Victor 1; Cánovas Peña, Jose Salvador 2

1 Universidad de Murcia, Departamento de Matemáticas, Campus de Espinardo, 30100 Murcia (Espagne)
2 Universidad Politécnica de Cartagena, Departamento de Matemática Aplicada, Paseo de Alfonso XIII 34-36, 30203 Cartagena (Espagne)
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Jiménez López, Victor; Cánovas Peña, Jose Salvador. Computing explicitly topological sequence entropy: the unimodal case. Annales de l'Institut Fourier, Volume 52 (2002) no. 4, pp. 1093-1133. doi : 10.5802/aif.1913. http://www.numdam.org/articles/10.5802/aif.1913/

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