HANTÁKOVÁ, Jana. Li-Yorke sensitivity does not imply Li-Yorke chaos. Ergodic Theory and Dynamical Systems. New York: Cambridge University Press, 2019, vol. 39, No 11, p. 3066-3074. ISSN 0143-3857. Available from: https://dx.doi.org/10.1017/etds.2018.10.
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Basic information
Original name Li-Yorke sensitivity does not imply Li-Yorke chaos
Authors HANTÁKOVÁ, Jana (203 Czech Republic, guarantor, belonging to the institution).
Edition Ergodic Theory and Dynamical Systems, New York, Cambridge University Press, 2019, 0143-3857.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW Ergodic Theory and Dynamical Systems
RIV identification code RIV/47813059:19610/19:A0000053
Organization unit Mathematical Institute in Opava
Doi http://dx.doi.org/10.1017/etds.2018.10
UT WoS 000488517300008
Keywords in English Li-Yorke sensitivity; Li-Yorke chaos; scrambled set
Tags MÚ
Tags International impact, Reviewed
Changed by Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 20/4/2020 15:59.
Abstract
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].
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