Article contents
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].
- Type
- Original Article
- Information
- Copyright
- © Cambridge University Press, 2018
References
- 2
- Cited by