Li-Yorke sensitivity does not imply Li-Yorke chaos

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F19%3AA0000053" target="_blank" >RIV/47813059:19610/19:A0000053 - isvavai.cz</a>
Result on the web
<a href="https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/liyorke-sensitivity-does-not-imply-liyorke-chaos/CBB1D9646D621F9443F154BA20C604A1" target="_blank" >https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/liyorke-sensitivity-does-not-imply-liyorke-chaos/CBB1D9646D621F9443F154BA20C604A1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/etds.2018.10" target="_blank" >10.1017/etds.2018.10</a>

Result language
angličtina
Original language name
Li-Yorke sensitivity does not imply Li-Yorke chaos
Original language description
We construct an infinite-dimensional compact metric space X, which is a closed subset of S x H, where S is the unit circle and H is the Hilbert cube, and a skew-product map F acting on X such that (X, F) is Li-Yorke sensitive but possesses at most countable scrambled sets. This disproves the conjecture of Akin and Kolyada that Li-Yorke sensitivity implies Li-Yorke chaos [Akin and Kolyada. Li-Yorke sensitivity. Nonlinearity 16, (2003), 1421-1433].
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
—
OECD FORD branch
10101 - Pure mathematics

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

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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