no. 4
Computing explicitly topological sequence entropy: the unimodal case
[Calcul explicite de l'entropie topologique séquentielle; le cas unimodal]
Jiménez López, Victor1 ; Cánovas Peña, Jose Salvador2
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)
Annales de l'Institut Fourier, Tome 52 (2002) no. 4, pp. 1093-1133.

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 ∞ .

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 f∈W(I) respect to the sequence D=(2 m-1 ) m=1 ∞ .

DOI : 10.5802/aif.1913
Classification : 37B40, 26A18, 54H20
Keywords: map of type $2^\infty $, topological sequence entropy, unimodal map
Mot clés : fonction de type $2^\infty $, entropie séquentielle topologique, fonction unimodale

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, Tome 52 (2002) no. 4, pp. 1093-1133. doi : 10.5802/aif.1913. https://aif.centre-mersenne.org/articles/10.5802/aif.1913/

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