科研之友
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摘要
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-Holder 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.
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单位广州航海高等专科学校
