  We construct an infinite-dimensional compact metric space $X$, which is a
closed subset of $\mathbb{S}\times\mathbb{H}$, where $\mathbb{S}$ is the unit
circle and $\mathbb{H}$ 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].
