Two Kinds of Chaos and Relations between them

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Two Kinds of Chaos and Relations between them

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Two Kinds of Chaos and Relations between them

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GP201%2F01%2FP134" target="_blank" >GP201/01/P134: Chaos v diskrétních dynamických systémech</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2003

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Acta Mathematica Universitatis Comenianae

ISSN

ISSN0862-9544

e-ISSN

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Svazek periodika

72

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

9

Strana od-do

119-12

Kód UT WoS článku

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EID výsledku v databázi Scopus

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