Doubling metric Diophantine approximation in the dynamical system of continued fractions

Lingling Huang

Chaos, Solitons & Fractals, 2018, vol. 106, issue C, 72-75

Abstract: This paper is concerned with the Diophantine properties of the orbits of real numbers in continued fraction system under the doubling metric. More precisely, let φ be a positive function defined on N. We determine the Lebesgue measure and Hausdorff dimension of the set E(φ)={(x,y)∈[0,1)×[0,1):|Tnx−y|<φ(n)fori.m.n},where T is the Gauss map and “i.m.” stands for “infinitely many”.

Keywords: Continued fraction system; Metric theory; Hausdorff dimension (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077917304642
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:106:y:2018:i:c:p:72-75

DOI: 10.1016/j.chaos.2017.11.007

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().