MEAN LI–YORKE CHAOTIC SET WITH FULL HAUSDORFF DIMENSION FOR CONTINUED FRACTIONS

Weibin Liu () and Shuailing Wang
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Weibin Liu: Department of Basic Courses, Guangzhou Maritime University, Guangzhou 510725, P. R. China
Shuailing Wang: ��Department of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 08, 1-9

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.

Keywords: Continued Fractions; Hausdorff Dimension; Mean Li–Yorke Chaotic (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21502583

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