Approximation properties of Lüroth expansions

Tan, Bo; Zhou, Qinglong

doi:10.3934/dcds.2020389

Cited by 7 publications

(2 citation statements)

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“…On the other hand, we refer the reader to [3,7] for a detailed account on the theory of Hausdorff dimension. Some newer results on Lüroth series and Hausdorff dimension can be found in [1,25,26].…”

Section: Preliminariesmentioning

confidence: 99%

“…We think that our choice is more natural, because the itinerary of any x ∈ (0, 1] with respect to L provides the inverse function of Λ and we do not have to mind the points whose orbit is eventually 0. Other recent developments in Lüroth series, such as [1,25,26], also use Galambos' approach, although the definition in [6] is precisely the one given by J. Lüroth in [21]. In any case, this difference affects only countably many points and hence is irrelevant to our discussion.…”

Section: So Our Statement Followsmentioning

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: Preliminariesmentioning

confidence: 99%