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

Sergiĭ Kolyada; Michał Misiurewicz; L’ubomír Snoha

Fundamenta Mathematicae (1999)

- Volume: 160, Issue: 2, page 161-181
- ISSN: 0016-2736

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topKolyada, Sergiĭ, Misiurewicz, Michał, and Snoha, L’ubomír. "Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval." Fundamenta Mathematicae 160.2 (1999): 161-181. <http://eudml.org/doc/212386>.

@article{Kolyada1999,

abstract = {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.},

author = {Kolyada, Sergiĭ, Misiurewicz, Michał, Snoha, L’ubomír},

journal = {Fundamenta Mathematicae},

keywords = {nonautonomous dynamical system; topological entropy; triangular maps; piecewise monotone maps; $C^∞$ maps; nonautonomous systems; discrete dynamical system; piecewise monotone dynamical systems},

language = {eng},

number = {2},

pages = {161-181},

title = {Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval},

url = {http://eudml.org/doc/212386},

volume = {160},

year = {1999},

}

TY - JOUR

AU - Kolyada, Sergiĭ

AU - Misiurewicz, Michał

AU - Snoha, L’ubomír

TI - Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval

JO - Fundamenta Mathematicae

PY - 1999

VL - 160

IS - 2

SP - 161

EP - 181

AB - 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.

LA - eng

KW - nonautonomous dynamical system; topological entropy; triangular maps; piecewise monotone maps; $C^∞$ maps; nonautonomous systems; discrete dynamical system; piecewise monotone dynamical systems

UR - http://eudml.org/doc/212386

ER -

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