Some chaotic and mixing properties of fuzzified dynamical systems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F14%3AA1500R9V" target="_blank" >RIV/61988987:17610/14:A1500R9V - 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
Some chaotic and mixing properties of fuzzified dynamical systems
Original language description
Let X be a compact metric space, let phi be a continuous self-map on X, and let F(X) denote the space of fuzzy sets on X equipped with the levelwise topology. In this paper we study relations between a given (crisp) dynamical system (X, phi) and its g-fuzzification (F(X), Phi(g)). Among other things we study various (weak, strong, mild etc.) mixing properties and also several kinds of chaotic behaviors (Li-Yorke chaos, omega-chaos, distributional chaos, topological chaos etc.). We specified subspaces offuzzy sets which make sense to study further. Additionally, we proved that numerous local characteristics of the original dynamical system can be found in its fuzzy extension, while many global characteristics are preserved in the opposite direction. Thus, among other things, we obtained easy-to-check criteria for checking absence of complex behavior in induced fuzzy dynamical systems.
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/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: IT4Innovations Centre of Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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