On two notions of fuzzy topological entropy

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On two notions of fuzzy topological entropy
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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