Balibrea, Francisco; Peña, Jose Salvador Cánovas; López, Víctor Jiménez
Commutativity and non-commutativity of topological sequence entropy
Annales de l'institut Fourier, Tome 49 (1999) no. 5 , p. 1693-1709
Zbl 0990.37010 | MR 2001g:37015 | 1 citation dans Numdam
doi : 10.5802/aif.1735
URL stable : http://www.numdam.org/item?id=AIF_1999__49_5_1693_0

Dans cet article nous étudions la propriété de commutativité pour l’entropie séquentielle topologique. Nous prouvons que si X est un espace métrique compact et f,g:XX sont deux fonctions continues, alors h A (fg)=h A (gf) pour toute suite croissance AX=[0,1] et nous construisons un contre-exemple dans le cas général. Au passage, nous prouvons aussi que l’égalité h A (f)=h A (f| n0 f n (X) ) est vraie si X=[0,1] mais ne l’est pas nécessairement si X est un espace métrique compact arbitraire.
In this paper we study the commutativity property for topological sequence entropy. We prove that if X is a compact metric space and f,g:XX are continuous maps then h A (fg)=h A (gf) for every increasing sequence A if X=[0,1], and construct a counterexample for the general case. In the interim, we also show that the equality h A (f)=h A (f| n0 f n (X) ) is true if X=[0,1] but does not necessarily hold if X is an arbitrary compact metric space.

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