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 
@article{10_4064_fm_160_2_161_181,
     author = {Sergi\u{i} Kolyada and Micha{\l} Misiurewicz and L{\textquoteright}ubom{\'\i}r Snoha},
     title = {Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval},
     journal = {Fundamenta Mathematicae},
     pages = {161--181},
     publisher = {mathdoc},
     volume = {160},
     number = {2},
     year = {1999},
     doi = {10.4064/fm-160-2-161-181},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-160-2-161-181/}
}
TY  - JOUR
AU  - Sergiĭ Kolyada
AU  - Michał Misiurewicz
AU  - L’ubomír Snoha
TI  - Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval
JO  - Fundamenta Mathematicae
PY  - 1999
SP  - 161
EP  - 181
VL  - 160
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-160-2-161-181/
DO  - 10.4064/fm-160-2-161-181
LA  - en
ID  - 10_4064_fm_160_2_161_181
ER  - 
%0 Journal Article
%A Sergiĭ Kolyada
%A Michał Misiurewicz
%A L’ubomír Snoha
%T Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval
%J Fundamenta Mathematicae
%D 1999
%P 161-181
%V 160
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-160-2-161-181/
%R 10.4064/fm-160-2-161-181
%G en
%F 10_4064_fm_160_2_161_181
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. http://geodesic.mathdoc.fr/articles/10.4064/fm-160-2-161-181/

Cité par Sources :