MLÍCHOVÁ, Michaela. Li-Yorke sensitive and weak mixing dynamical systems. Journal of Difference Equations and Applications. Abingdon: Taylor and Francis Ltd., 2018, vol. 24, No 5, p. 667-674. ISSN 1023-6198. Available from: https://dx.doi.org/10.1080/10236198.2017.1304545.
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Basic information
Original name Li-Yorke sensitive and weak mixing dynamical systems
Authors MLÍCHOVÁ, Michaela (203 Czech Republic, guarantor, belonging to the institution).
Edition Journal of Difference Equations and Applications, Abingdon, Taylor and Francis Ltd. 2018, 1023-6198.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United Kingdom of Great Britain and Northern Ireland
Confidentiality degree is not subject to a state or trade secret
WWW Journal of Difference Equations and Applications
RIV identification code RIV/47813059:19610/18:A0000028
Organization unit Mathematical Institute in Opava
Doi http://dx.doi.org/10.1080/10236198.2017.1304545
UT WoS 000427557900003
Keywords in English Li-Yorke sensitivity; weak mixing system; extension of system; skew-product
Tags International impact, Reviewed
Changed by Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 3/4/2019 12:56.
Abstract
Akin and Kolyada in 2003 [E. Akin, S. Kolyada, Li–Yorke sensitivity, Nonlinearity 16 (2003), pp. 1421–1433] introduced the notion of Li–Yorke sensitivity. They proved that every weak mixing system (X, T), where X is a compact metric space and T a continuous map of X is Li–Yorke sensitive. An example of Li–Yorke sensitive system without weak mixing factors was given in [M. Čiklová, Li–Yorke sensitive minimal maps, Nonlinearity 19 (2006), pp. 517–529] (see also [M. Čiklová-Mlíchová, Li–Yorke sensitive minimal maps II, Nonlinearity 22 (2009), pp. 1569–1573]). In their paper, Akin and Kolyada conjectured that every minimal system with a weak mixing factor, is Li–Yorke sensitive. We provide arguments supporting this conjecture though the proof seems to be difficult.
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