Necessity of the third condition from the definition of omega chaos

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F15%3A86095873" target="_blank" >RIV/61989100:27240/15:86095873 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27740/15:86095873

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Necessity of the third condition from the definition of omega chaos

Popis výsledku v původním jazyce

The notion of omega chaos was introduced by S. Li in 1993 for continuous maps of compact metric spaces by three conditions: 1. the set difference of omega limit sets is uncountable, 2. intersection of omega limit sets is nonempty and 3. each omega limitset of the point from the omega scrambled set is not contained in the set of all periodic points. It was also pointed that the third condition is superfluous for continuous maps of the compact interval. As a main result of this paper it will be shown that the third condition is essential even in one dimension by construction of two examples of homeomorphisms on one dimensional arcwise connected space having two point set or infinite respectively that satisfies first and second condition but the third condition is not fulfilled from the definition of omega chaos.

Název v anglickém jazyce

Necessity of the third condition from the definition of omega chaos

Popis výsledku anglicky

The notion of omega chaos was introduced by S. Li in 1993 for continuous maps of compact metric spaces by three conditions: 1. the set difference of omega limit sets is uncountable, 2. intersection of omega limit sets is nonempty and 3. each omega limitset of the point from the omega scrambled set is not contained in the set of all periodic points. It was also pointed that the third condition is superfluous for continuous maps of the compact interval. As a main result of this paper it will be shown that the third condition is essential even in one dimension by construction of two examples of homeomorphisms on one dimensional arcwise connected space having two point set or infinite respectively that satisfies first and second condition but the third condition is not fulfilled from the definition of omega chaos.

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

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Applied Mathematics and Information Sciences

ISSN

1935-0090

e-ISSN

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Svazek periodika

9

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

5

Strana od-do

2303-2307

Kód UT WoS článku

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EID výsledku v databázi Scopus

2-s2.0-84937954109