2017/11/29 by Hantáková, Jana
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1711.10763
We construct an infinite-dimensional compact metric space X, which is a closed subset of \mathbbS×ℍ, where \mathbbS 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 from the article [Akin E., Kolyada S., Li-Yorke sensitivity, Nonlinearity 16, (2003), 1421-1433].