Abstract
<abstract><p>In this paper, we investigate mean Li-Yorke chaos along some sequence and Li-Yorke chaos for cookie-cutter systems. By applying bounded distortion and a locally $ \alpha $-H$ \ddot{\rm{o}} $lder condition, we show that the cookie-cutter set contains a mean Li-Yorke scrambled set along some sequence in which the Hausdorff dimension equals the Hausdorff dimension of the cookie-cutter set. That is to say, a cookie-cutter system is mean Li-Yorke chaotic along some sequence. Meanwhile, we proved that every mean Li-Yorke scrambled set is also a scrambled set; hence a cookie-cutter system is also Li-Yorke chaotic.</p></abstract>
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