Inheriting of chaos in uniformly convergent nonautonomous dynamical systems on the interval
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F16%3A%230000512" target="_blank" >RIV/47813059:19610/16:#0000512 - isvavai.cz</a>
Result on the web
<a href="http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=12130" target="_blank" >http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=12130</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcds.2016.36.3435" target="_blank" >10.3934/dcds.2016.36.3435</a>
Alternative languages
Result language
angličtina
Original language name
Inheriting of chaos in uniformly convergent nonautonomous dynamical systems on the interval
Original language description
We consider nonautonomous discrete dynamical systems {f(n)}(n >= 1), where every f(n) is a surjective continuous map [0, 1] -> [0, 1] such that f(n) converges uniformly to a map f. It is well-known that f has positive topological entropy iff {f(n)}(n >=1), has. On the other hand, for systems with zero topological entropy, {f(n)}(n >= 1), with very complex dynamics can converge even to the identity map. We study the following question: Which properties of the limit function f are inherited by nonautonomous system {f(n)}(n >= 1)? We show that Li-Yorke chaos, distributional chaos DC1 and, for zero entropy maps, infinite omega-limit sets are inherited by nonautonomous systems and, for zero entropy maps, we give a criterion on f under which {f(n)}(n >= 1)is DC1. More precisely, our main results are: (i) If f is Li-Yorke chaotic then {f(n)}(n >= 1) is Li-Yorke chaotic as well, and the analogous implication is true for distributional chaos DC1; (ii) If f has zero topological entropy then th
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP201%2F10%2F0887" target="_blank" >GAP201/10/0887: Discrete dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Continuous Dynamical Systems - Series A
ISSN
1078-0947
e-ISSN
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Volume of the periodical
36
Issue of the periodical within the volume
6
Country of publishing house
US - UNITED STATES
Number of pages
9
Pages from-to
3435-3443
UT code for WoS article
000371998300020
EID of the result in the Scopus database
2-s2.0-84954286229