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# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval

### Tom 160 / 1999

Fundamenta Mathematicae 160 (1999), 161-181 DOI: 10.4064/fm-160-2-161-181

#### Streszczenie

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.