Chaotic and topological properties of continued fractions

Liu, Weibin; Li, Bing

doi:10.1016/j.jnt.2016.10.019

Cited by 10 publications

(4 citation statements)

References 25 publications

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“…Main results and structure of the paper. Lately, W. Liu, B. Li and S. Wang in [19,20] studied the chaotic properties of ([0, 1), G ). In the following statement, we summarise [19,Theorem 1.3,Corollary 1.4] and [20,Theorem 1.1,1.2].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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Chaotic sets and Hausdorff dimension for Lüroth expansions

Barrera,

Robert

2021

Preprint

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Regular continued fraction expansions and Lüroth series of real numbers within the unit interval share several properties, although they are generated by different dynamical systems. Our research provides new similarities between both sets of expansions in terms of topological dynamics and Hausdorff dimension. In particular, we establish a complete analogue with the results of W. Liu, B. Li and S. Wang in [19,20] on the distal, asymptotic and Li-Yorke pairs for the Gauss map, in the case of the Lüroth transformation.

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…Recall that Theorems A, B, and D are full analogues of the main results in [19], [20]. It is thus natural to pose the problems above for ([0, 1), G ), where G is the usual Gauss map.…”

Section: Further Problemsmentioning

confidence: 99%

Chaotic sets and Hausdorff dimension for Lüroth expansions

Barrera,

Robert

2021

Preprint

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“…In [7], Bruin and Jiménez López studied the Lebesgue measure of scrambled sets for C 2 and C 3 multimodal interval maps f with non-flat critical points. Recently, in [17] Liu and Li constructed a scrambled set with full Hausdorff dimension for the Gauss system.…”

Section: Introductionmentioning

confidence: 99%

The Hausdorff dimension of multiply Xiong chaotic sets

Lü

Xiao

2019

Ergod. Th. Dynam. Sys.

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“…In [13], the author constructed a Xiong chaotic with full topological entropy everywhere for positively expansive systems with specification property. Recently, in [16], Liu and Li constructed a scrambled set with full Hausdorff dimension for the Gauss system.…”

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confidence: 99%

Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for \beta -transformation

Xiao¹

2021

Discrete &Amp; Continuous Dynamical Systems - A

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We construct a mean Li-Yorke chaotic set along polynomial sequences (the degree of this polynomial is not less than three) with full Hausdorff dimension and full topological entropy for β-transformation. An uncountable subset C is said to be a mean Li-Yorke chaotic set along sequence {an}, if both lim inf N →∞ 1 N N j=1 d(f a j (x), f a j (y)) = 0 and lim sup N →∞ 1 N N j=1 d(f a j (x), f a j (y)) > 0 hold for any two distinct points x and y in C.

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Chaotic and topological properties of continued fractions

Abstract: Abstract. We prove that there exists a scrambled set for the Gauss map with full Hausdorff dimension. Meanwhile, we also investigate the topological properties of the sets of points with dense or non-dense orbits.

Cited by 10 publications

References 25 publications

Chaotic sets and Hausdorff dimension for Lüroth expansions

Chaotic sets and Hausdorff dimension for Lüroth expansions

The Hausdorff dimension of multiply Xiong chaotic sets

Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for \beta -transformation

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