no. 5
Commutativity and non-commutativity of topological sequence entropy
Annales de l'Institut Fourier, Tome 49 (1999) no. 5, pp. 1693-1709.

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:X→X sont deux fonctions continues, alors h A (f∘g)=h A (g∘f) pour toute suite croissance A où X=[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| ∩ n≥0 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:X→X are continuous maps then h A (f∘g)=h A (g∘f) 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| ∩ n≥0 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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     author = {Balibrea, Francisco and Pe\~na, Jose Salvador C\'anovas and L\'opez, V{\'\i}ctor Jim\'enez},
     title = {Commutativity and non-commutativity of topological sequence entropy},
     journal = {Annales de l'Institut Fourier},
     pages = {1693--1709},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {49},
     number = {5},
     year = {1999},
     doi = {10.5802/aif.1735},
     zbl = {0990.37010},
     mrnumber = {2001g:37015},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1735/}
}
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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, pp. 1693-1709. doi : 10.5802/aif.1735. https://aif.centre-mersenne.org/articles/10.5802/aif.1735/

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