Li-Yorke sensitive and weak mixing dynamical systems

@article{30466,
   author = {Mlíchová, Michaela},
   article_location = {Abingdon},
   article_number = {5},
   doi = {http://dx.doi.org/10.1080/10236198.2017.1304545},
   keywords = {Li-Yorke sensitivity; weak mixing system; extension of system; skew-product},
   language = {eng},
   issn = {1023-6198},
   journal = {Journal of Difference Equations and Applications},
   title = {Li-Yorke sensitive and weak mixing dynamical systems},
   url = {https://www.tandfonline.com/doi/full/10.1080/10236198.2017.1304545},
   volume = {24},
   year = {2018}
}

TY  - JOUR
ID  - 30466
AU  - Mlíchová, Michaela
PY  - 2018
TI  - Li-Yorke sensitive and weak mixing dynamical systems
JF  - Journal of Difference Equations and Applications
VL  - 24
IS  - 5
SP  - 667-674
EP  - 667-674
PB  - Taylor and Francis Ltd.
SN  - 10236198
KW  - Li-Yorke sensitivity
KW  - weak mixing system
KW  - extension of system
KW  - skew-product
UR  - https://www.tandfonline.com/doi/full/10.1080/10236198.2017.1304545
L2  - https://www.tandfonline.com/doi/full/10.1080/10236198.2017.1304545
N2  - 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.
ER  - 

MLÍCHOVÁ, Michaela. Li-Yorke sensitive and weak mixing dynamical systems. \textit{Journal of Difference Equations and Applications}. Abingdon: Taylor and Francis Ltd., 2018, roč.~24, č.~5, s.~667-674. ISSN~1023-6198. Dostupné z: https://dx.doi.org/10.1080/10236198.2017.1304545.