Standard

Natural extensions for Nakada's α-expansions : Descending from 1 to g2. / de Jonge, Jaap; Kraaikamp, Cornelis.

In: Journal of Number Theory, Vol. 183, 02.2018, p. 172-212.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

APA

Vancouver

Author

BibTeX

@article{c61d1b76deac4589a6aaa3f6e11ec256,
title = "Natural extensions for Nakada's α-expansions: Descending from 1 to g2",
abstract = "By means of singularisations and insertions in Nakada's α-expansions, which involves the removal of partial quotients 1 while introducing partial quotients with a minus sign, the natural extension of Nakada's continued fraction map Tα is given for (10-2)/3≤α<1. From our construction it follows that Ωα, the domain of the natural extension of Tα, is metrically isomorphic to Ωg for α∈[g2,g), where g is the small golden mean. Finally, although Ωα proves to be very intricate and unmanageable for α∈[g2,(10-2)/3), the α-Legendre constant L(α) on this interval is explicitly given.",
keywords = "Continued fractions, Metric theory",
author = "{de Jonge}, Jaap and Cornelis Kraaikamp",
note = "Author accepted manuscript",
year = "2018",
month = "2",
doi = "10.1016/j.jnt.2017.07.012",
language = "English",
volume = "183",
pages = "172--212",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Natural extensions for Nakada's α-expansions

T2 - Journal of Number Theory

AU - de Jonge, Jaap

AU - Kraaikamp, Cornelis

N1 - Author accepted manuscript

PY - 2018/2

Y1 - 2018/2

N2 - By means of singularisations and insertions in Nakada's α-expansions, which involves the removal of partial quotients 1 while introducing partial quotients with a minus sign, the natural extension of Nakada's continued fraction map Tα is given for (10-2)/3≤α<1. From our construction it follows that Ωα, the domain of the natural extension of Tα, is metrically isomorphic to Ωg for α∈[g2,g), where g is the small golden mean. Finally, although Ωα proves to be very intricate and unmanageable for α∈[g2,(10-2)/3), the α-Legendre constant L(α) on this interval is explicitly given.

AB - By means of singularisations and insertions in Nakada's α-expansions, which involves the removal of partial quotients 1 while introducing partial quotients with a minus sign, the natural extension of Nakada's continued fraction map Tα is given for (10-2)/3≤α<1. From our construction it follows that Ωα, the domain of the natural extension of Tα, is metrically isomorphic to Ωg for α∈[g2,g), where g is the small golden mean. Finally, although Ωα proves to be very intricate and unmanageable for α∈[g2,(10-2)/3), the α-Legendre constant L(α) on this interval is explicitly given.

KW - Continued fractions

KW - Metric theory

UR - http://www.scopus.com/inward/record.url?scp=85028811266&partnerID=8YFLogxK

UR - http://resolver.tudelft.nl/uuid:c61d1b76-deac-4589-a6aa-a3f6e11ec256

U2 - 10.1016/j.jnt.2017.07.012

DO - 10.1016/j.jnt.2017.07.012

M3 - Article

VL - 183

SP - 172

EP - 212

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -

ID: 30801241