Renewal-type Limit Theorem for the Gauss map and continued fractions

YG Sinai; C Ulcigrai

doi:10.1017/S0143385707000466

Renewal-type Limit Theorem for the Gauss map and continued fractions

YG Sinai
, C Ulcigrai

Research output: Contribution to journal › Article (Academic Journal) › peer-review

16 Citations (Scopus)

Abstract

In this paper we prove a renewal-type limit theorem. Given and R>0, let qnR be the first denominator of the convergents of α 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.

Translated title of the contribution	Renewal-type Limit Theorem for the Gauss map and continued fractions
Original language	English
Pages (from-to)	643 - 655
Number of pages	13
Journal	Ergodic Theory and Dynamical Systems
Volume	28, no 2
DOIs	https://doi.org/10.1017/S0143385707000466
Publication status	Published - Apr 2008

Bibliographical note

Publisher: Cambridge University Press

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10.1017/S0143385707000466

http://arxiv.org/abs/0710.1283

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title = "Renewal-type Limit Theorem for the Gauss map and continued fractions",

abstract = "In this paper we prove a renewal-type limit theorem. Given and R>0, let qnR be the first denominator of the convergents of α 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 = "YG Sinai and C Ulcigrai",

note = "Publisher: Cambridge University Press",

year = "2008",

month = apr,

doi = "10.1017/S0143385707000466",

language = "English",

volume = "28, no 2",

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journal = "Ergodic Theory and Dynamical Systems",

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T1 - Renewal-type Limit Theorem for the Gauss map and continued fractions

AU - Sinai, YG

AU - Ulcigrai, C

N1 - Publisher: Cambridge University Press

PY - 2008/4

Y1 - 2008/4

N2 - In this paper we prove a renewal-type limit theorem. Given and R>0, let qnR be the first denominator of the convergents of α 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 and R>0, let qnR be the first denominator of the convergents of α 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.

U2 - 10.1017/S0143385707000466

DO - 10.1017/S0143385707000466

M3 - Article (Academic Journal)

SN - 1469-4417

VL - 28, no 2

SP - 643

EP - 655

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

ER -

Renewal-type Limit Theorem for the Gauss map and continued fractions

Abstract

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