In this paper we study the commutativity property for topological sequence entropy. We prove that if is a compact metric space and are continuous maps then for every increasing sequence if , and construct a counterexample for the general case. In the interim, we also show that the equality is true if but does not necessarily hold if is an arbitrary compact metric space.
Dans cet article nous étudions la propriété de commutativité pour l’entropie séquentielle topologique. Nous prouvons que si est un espace métrique compact et sont deux fonctions continues, alors pour toute suite croissance où et nous construisons un contre-exemple dans le cas général. Au passage, nous prouvons aussi que l’égalité est vraie si mais ne l’est pas nécessairement si est un espace métrique compact arbitraire.
@article{AIF_1999__49_5_1693_0, 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}, mrnumber = {2001g:37015}, zbl = {0990.37010}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1735/} }
TY - JOUR AU - Balibrea, Francisco AU - Peña, Jose Salvador Cánovas AU - López, Víctor Jiménez TI - Commutativity and non-commutativity of topological sequence entropy JO - Annales de l'Institut Fourier PY - 1999 SP - 1693 EP - 1709 VL - 49 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1735/ DO - 10.5802/aif.1735 LA - en ID - AIF_1999__49_5_1693_0 ER -
%0 Journal Article %A Balibrea, Francisco %A Peña, Jose Salvador Cánovas %A López, Víctor Jiménez %T Commutativity and non-commutativity of topological sequence entropy %J Annales de l'Institut Fourier %D 1999 %P 1693-1709 %V 49 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1735/ %R 10.5802/aif.1735 %G en %F AIF_1999__49_5_1693_0
Balibrea, Francisco; Peña, Jose Salvador Cánovas; López, Víctor Jiménez. Commutativity and non-commutativity of topological sequence entropy. Annales de l'Institut Fourier, Volume 49 (1999) no. 5, pp. 1693-1709. doi : 10.5802/aif.1735. http://archive.numdam.org/articles/10.5802/aif.1735/
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