On generic and dense chaos for maps induced on hyperspaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F18%3AA0000029" target="_blank" >RIV/47813059:19610/18:A0000029 - isvavai.cz</a>
Result on the web
<a href="https://www.tandfonline.com/doi/full/10.1080/10236198.2017.1309035" target="_blank" >https://www.tandfonline.com/doi/full/10.1080/10236198.2017.1309035</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/10236198.2017.1309035" target="_blank" >10.1080/10236198.2017.1309035</a>

Result language
angličtina
Original language name
On generic and dense chaos for maps induced on hyperspaces
Original language description
A continuous map f on a compact metric space X induces in a natural way the map f’ on the hyperspace K(X) of all closed non-empty subsets of X. We study the question of transmission of chaos between f and f’. We deal with generic, generic e-, dense and dense e-chaos for interval maps. We prove that all four types of chaos transmit from f to f, while the converse transmission from f to f’ is true for generic, generic e-and dense e-chaos. Moreover, the transmission of dense eand generic e-chaos from f’ to f is true for maps on general compact metric spaces.
Czech name
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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
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OECD FORD branch
10101 - Pure mathematics

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

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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