Geodesic
Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval
Fundamenta Mathematicae, Tome 160 (1999) no. 2, pp. 161-181

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The topological entropy of a nonautonomous dynamical system given by a sequence of compact metric spaces $(X_i)^∞_{i = 1}$ and a sequence of continuous maps $(f_i)^∞_{i = 1}$, $f_i : X_i → X_{i+1}$, is defined. If all the spaces are compact real intervals and all the maps are piecewise monotone then, under some additional assumptions, a formula for the entropy of the system is obtained in terms of the number of pieces of monotonicity of $f_n ○... ○ f_2 ○ f_1$. As an application we construct a large class of smooth triangular maps of the square of type $2^∞$ and positive topological entropy.
DOI : 10.4064/fm-160-2-161-181
Keywords: nonautonomous dynamical system, topological entropy, triangular maps, piecewise monotone maps, $C^∞$ maps

Sergiĭ Kolyada 1 ; Michał Misiurewicz 1 ; L’ubomír Snoha 1

1 
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Sergiĭ Kolyada; Michał Misiurewicz; L’ubomír Snoha. Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval. Fundamenta Mathematicae, Tome 160 (1999) no. 2, pp. 161-181. doi: 10.4064/fm-160-2-161-181

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