On the recurrence rates of continued fractions

Chun Wei, Min Wu and Shuailing Wang

Chaos, Solitons & Fractals, 2018, vol. 114, issue C, 474-477

Abstract: Letting T be Gauss transformation on [0,1), we consider the first return time τn(x) of x ∈ [0, 1) to the cylinder of order n containing x. We prove that the Hausdorff dimension of the set {x∈[0,1):lim infn→∞logτn(x)φ(n)=α,lim supn→∞logτn(x)φ(n)=γ}is either zero or one depending on φ, α and γ, where φ: N→R+ is a monotonically increasing function and 0≤α≤γ≤+∞.

Keywords: Continued fraction; Recurrence rates; Hausdorff dimension (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:114:y:2018:i:c:p:474-477

DOI: 10.1016/j.chaos.2018.07.027

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