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@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, 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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