Two Kinds of Chaos and Relations between them

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F03%3A00000116" target="_blank" >RIV/47813059:19610/03:00000116 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Two Kinds of Chaos and Relations between them
Original language description
In this paper we consider relations between chaos in the sense of Li and Yorke, and $omega$-chaos. The main aim is to show how important the size of scrambled sets is in definitions of chaos. We provide an example of an $omega$-chaotic map on a compactmetric space which is chaotic in the sense of Li and Yorke, but any scrambled set contains only two points. Chaos in the sense of Li and Yorke cannot be excluded: We show that any continuous map of a compact metric space which is $omega$-chaotic, mustbe chaotic in the sense of Li and Yorke. Since it is known that, for continuous maps of the interval, Li and Yorke chaos does not imply $omega$-chaos, Li and Yorke chaos on compact metric spaces appears to be weaker. We also consider, among others, therelations of the two notions of chaos on countably infinite compact spaces.
Czech name
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Czech description
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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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Project
<a href="/en/project/GP201%2F01%2FP134" target="_blank" >GP201/01/P134: Chaos in discrete dynamical systems</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2003
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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