Li-Yorke sensitivity does not imply Li-Yorke chaos

@article{32742,
   author = {Hantáková, Jana},
   article_location = {New York},
   article_number = {11},
   doi = {http://dx.doi.org/10.1017/etds.2018.10},
   keywords = {Li-Yorke sensitivity; Li-Yorke chaos; scrambled set},
   language = {eng},
   issn = {0143-3857},
   journal = {Ergodic Theory and Dynamical Systems},
   title = {Li-Yorke sensitivity does not imply Li-Yorke chaos},
   url = {https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/liyorke-sensitivity-does-not-imply-liyorke-chaos/CBB1D9646D621F9443F154BA20C604A1},
   volume = {39},
   year = {2019}
}

TY  - JOUR
ID  - 32742
AU  - Hantáková, Jana
PY  - 2019
TI  - Li-Yorke sensitivity does not imply Li-Yorke chaos
JF  - Ergodic Theory and Dynamical Systems
VL  - 39
IS  - 11
SP  - 3066-3074
EP  - 3066-3074
PB  - Cambridge University Press
SN  - 01433857
KW  - Li-Yorke sensitivity
KW  - Li-Yorke chaos
KW  - scrambled set
UR  - https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/liyorke-sensitivity-does-not-imply-liyorke-chaos/CBB1D9646D621F9443F154BA20C604A1
L2  - https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/liyorke-sensitivity-does-not-imply-liyorke-chaos/CBB1D9646D621F9443F154BA20C604A1
N2  - 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].
ER  - 

HANTÁKOVÁ, Jana. Li-Yorke sensitivity does not imply Li-Yorke chaos. \textit{Ergodic Theory and Dynamical Systems}. New York: Cambridge University Press, roč.~39, č.~11, s.~3066-3074. ISSN~0143-3857. doi:10.1017/etds.2018.10. 2019.