Geodesic
ON TOPOLOGICAL SEQUENCE ENTROPY AND CHAOTIC MAPS ON INVERSE LIMIT SPACES
Acta mathematica Universitatis Comenianae, Tome 68 (1999) no. 2 
J. S. Canovas. ON TOPOLOGICAL SEQUENCE ENTROPY AND CHAOTIC MAPS ON INVERSE LIMIT SPACES. Acta mathematica Universitatis Comenianae, Tome 68 (1999) no. 2. http://geodesic.mathdoc.fr/item/AMUC_1999_68_2_a1/
@article{AMUC_1999_68_2_a1,
     author = {J. S. Canovas},
     title = {ON {TOPOLOGICAL} {SEQUENCE} {ENTROPY} {AND} {CHAOTIC} {MAPS} {ON} {INVERSE} {LIMIT} {SPACES}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1999},
     volume = {68},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1999_68_2_a1/}
}
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Voir la notice de l'article provenant de la source Comenius University

The aim of this paper is to prove the following results: a continuous map $% f\:[0,1]\rightarrow [0,1]$ is chaotic iff the shift map $\sigma _f\:\lim\limits_\leftarrow ([0,1],f)\rightarrow \lim\limits_\leftarrow ([0,1],f)$ is chaotic. However, this result fails, in general, for arbitrary compact metric spaces. $\sigma _f\:\lim\limits_\leftarrow ([0,1],f)\rightarrow \lim\limits_\leftarrow ([0,1],f)$ is chaotic iff there exists an increasing sequence of positive integers $A$ such that the topological sequence entropy $h_A(\sigma _f)>0$. Finally, for any $A$ there exists a chaotic continuous map $f_A\:[0,1]\rightarrow [0,1]$ such that $% h_A(\sigma _f_A)=0.$