Mean Li-Yorke chaotic set with full Hausdorff dimension for continued fractions. (English) Zbl 1498.37038
Summary: 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.
MSC:
| 37C45 | Dimension theory of smooth dynamical systems |
| 28A80 | Fractals |
| 11A55 | Continued fractions |
| 40A15 | Convergence and divergence of continued fractions |
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