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

YG Sinai, C Ulcigrai

Research output: Contribution to journalArticle (Academic Journal)peer-review

14 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 contributionRenewal-type Limit Theorem for the Gauss map and continued fractions
Original languageEnglish
Pages (from-to)643 - 655
Number of pages13
JournalErgodic Theory and Dynamical Systems
Volume28, no 2
DOIs
Publication statusPublished - Apr 2008

Bibliographical note

Publisher: Cambridge University Press

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