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

Yakov G. Sinai, Corinna Ulcigrai

Research output: Contribution to journalArticle

13 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 languageEnglish (US)
Pages (from-to)643-655
Number of pages13
JournalErgodic Theory and Dynamical Systems
Volume28
Issue number2
DOIs
StatePublished - Apr 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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