Renewal-type limit theorem for the Gauss map and continued fractions

Yakov G. Sinai; Corinna Ulcigrai

doi:10.1017/S0143385707000466

Renewal-type limit theorem for the Gauss map and continued fractions

Yakov G. Sinai, Corinna Ulcigrai

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

In this paper we prove a renewal-type limit theorem. Given α \in (0,1)\backslash \mathbb {Q} and R>0, let qnR be the first denominator of the convergents of which exceeds R. The main result in the paper is that the ratio qnR/R has a limiting distribution as R tends to infinity. The existence of the limiting distribution uses mixing of a special flow over the natural extension of the Gauss map.

Original language	English (US)
Pages (from-to)	643-655
Number of pages	13
Journal	Ergodic Theory and Dynamical Systems
Volume	28
Issue number	2
DOIs	https://doi.org/10.1017/S0143385707000466
State	Published - Apr 2008

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Access to Document

10.1017/S0143385707000466

Cite this

@article{dccffb593d0646c88a529c407fdaa268,

title = "Renewal-type limit theorem for the Gauss map and continued fractions",

abstract = "In this paper we prove a renewal-type limit theorem. Given α \in (0,1)\backslash \mathbb {Q} and R>0, let qnR be the first denominator of the convergents of which exceeds R. The main result in the paper is that the ratio qnR/R has a limiting distribution as R tends to infinity. The existence of the limiting distribution uses mixing of a special flow over the natural extension of the Gauss map.",

author = "Sinai, {Yakov G.} and Corinna Ulcigrai",

year = "2008",

month = apr,

doi = "10.1017/S0143385707000466",

language = "English (US)",

volume = "28",

pages = "643--655",

journal = "Ergodic Theory and Dynamical Systems",

issn = "0143-3857",

publisher = "Cambridge University Press",

number = "2",

}

TY - JOUR

T1 - Renewal-type limit theorem for the Gauss map and continued fractions

AU - Sinai, Yakov G.

AU - Ulcigrai, Corinna

PY - 2008/4

Y1 - 2008/4

N2 - In this paper we prove a renewal-type limit theorem. Given α \in (0,1)\backslash \mathbb {Q} and R>0, let qnR be the first denominator of the convergents of which exceeds R. The main result in the paper is that the ratio qnR/R has a limiting distribution as R tends to infinity. The existence of the limiting distribution uses mixing of a special flow over the natural extension of the Gauss map.

AB - In this paper we prove a renewal-type limit theorem. Given α \in (0,1)\backslash \mathbb {Q} and R>0, let qnR be the first denominator of the convergents of which exceeds R. The main result in the paper is that the ratio qnR/R has a limiting distribution as R tends to infinity. The existence of the limiting distribution uses mixing of a special flow over the natural extension of the Gauss map.

UR - http://www.scopus.com/inward/record.url?scp=43449085542&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43449085542&partnerID=8YFLogxK

U2 - 10.1017/S0143385707000466

DO - 10.1017/S0143385707000466

M3 - Article

AN - SCOPUS:43449085542

SN - 0143-3857

VL - 28

SP - 643

EP - 655

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 2

ER -

Renewal-type limit theorem for the Gauss map and continued fractions

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this