On two notions of fuzzy topological entropy

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA24029ND" target="_blank" >RIV/61988987:17610/23:A24029ND - isvavai.cz</a>
Výsledek na webu
<a href="https://www.sciencedirect.com/science/article/pii/S0165011422001518" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011422001518</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2022.04.005" target="_blank" >10.1016/j.fss.2022.04.005</a>

Jazyk výsledku
angličtina
Název v původním jazyce
On two notions of fuzzy topological entropy
Popis výsledku v původním jazyce
We explore the notion of fuzzy topological entropy when different definitions of fuzzy compactness are considered. We prove that the recent definitions by Tok and by Uzzal Afsan and Basu are not the most appropriate since they always display zero entropy. We give a simple proof of the bridge result which states that topological entropy agrees with fuzzy topological entropy when it is defined by using Lowen's definition of compactness. Consequently, many natural properties of the fuzzy topological entropy (such as monotonicity) are obtained as direct corollaries. The particular case of interval maps is also briefly discussed.
Název v anglickém jazyce
On two notions of fuzzy topological entropy
Popis výsledku anglicky
We explore the notion of fuzzy topological entropy when different definitions of fuzzy compactness are considered. We prove that the recent definitions by Tok and by Uzzal Afsan and Basu are not the most appropriate since they always display zero entropy. We give a simple proof of the bridge result which states that topological entropy agrees with fuzzy topological entropy when it is defined by using Lowen's definition of compactness. Consequently, many natural properties of the fuzzy topological entropy (such as monotonicity) are obtained as direct corollaries. The particular case of interval maps is also briefly discussed.

Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění
2023
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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