Chaos for multivalued maps and induced hyperspace maps

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73602187" target="_blank" >RIV/61989592:15310/20:73602187 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0960077920302988" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0960077920302988</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.chaos.2020.109898" target="_blank" >10.1016/j.chaos.2020.109898</a>

Result language
angličtina
Original language name
Chaos for multivalued maps and induced hyperspace maps
Original language description
Let (X, d) be a compact metric space and phi: X(sic)X be a multivalued map. At first, we will extend for these maps the notions of a topological entropy and Robinson's chaos from a single-valued into a multivalued setting and show their basic properties. Then, for a subclass of multivalued continuous maps with compact values, we will clarify their relationship to the induced (hyper)maps phi* : K(X) -> K(X) in the hyperspace (K(X), d(H)), endowed with the Hausdorff metric d(H), where K(X) consists of all compact subsets of X. Concretely, we will show that a positive topological entropy h(phi) of phi implies a positive topological entropy h(phi*) of phi*. On the other hand, Robinson's chaos to phi* implies in a reverse way Robinson's chaos to phi.
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

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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