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

14 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

Mathematics(all)
Applied Mathematics

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10.1017/S0143385707000466

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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 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",

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AU - Ulcigrai, Corinna

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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.

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

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