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Li–Yorke sensitivity does not imply Li–Yorke chaos
Published online by Cambridge University Press: 06 March 2018
Abstract
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 [Akin and Kolyada. Li–Yorke sensitivity. Nonlinearity16, (2003), 1421–1433].
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- © Cambridge University Press, 2018
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