On the centre and the set of omega-limit points of continuous maps on dendrites

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F09%3A%230000258" target="_blank" >RIV/47813059:19610/09:#0000258 - 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
On the centre and the set of omega-limit points of continuous maps on dendrites
Original language description
It is well known that for dynamical systems generated by continuous maps of a graph, the centre of the dynamical system is a subset of the set of omega-limit points. In this paper we provide an example of a continuous self-map f(1) of a dendrite such that omega(f(1)) is a proper subset of C(f(1)). The second example is a continuous self-map f(2) of a dendrite having a strictly increasing sequence of omega-limit sets which is not contained in any maximal one. Again, this is impossible for continuous mapson graphs.
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/GA201%2F06%2F0318" target="_blank" >GA201/06/0318: Dynamical Systems III</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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