Necessity of the third condition from the definition of omega chaos

Result code in 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>
Alternative codes found
RIV/61989100:27740/15:86095873
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Necessity of the third condition from the definition of omega chaos
Original language description
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.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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