Mean Li–yorke Chaotic Set With Full Hausdorff Dimension for Continued Fractions

Liu, Weibin; Wang, Shuailing

doi:10.1142/s0218348x21502583

Fractals

2021

DOI: 10.1142/s0218348x21502583

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Mean Li–yorke Chaotic Set With Full Hausdorff Dimension for Continued Fractions

Weibin Liu

Shuailing Wang

Abstract: In this paper, we consider the mean Li–Yorke chaotic property for continued fraction dynamical system. Every measurable mean Li–Yorke scrambled set along any given sequence is of zero Lebesgue measure. Meanwhile, we construct one with full Hausdorff dimension for the sequence with some mild condition.

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2022

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Li-Yorke chaotic property of cookie-cutter systems

Liu

2022

MATH

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<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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Li-Yorke chaotic property of cookie-cutter systems

Liu

2022

MATH

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Mean Li–yorke Chaotic Set With Full Hausdorff Dimension for Continued Fractions

Cited by 1 publication

References 40 publications

Li-Yorke chaotic property of cookie-cutter systems

Li-Yorke chaotic property of cookie-cutter systems

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