2007/10/05 by Yakov G. Sinai, Corinna Ulcigrai, Sinai, Yakov G. +1 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #math.DS
paper · pdf · doi:10.48550/arxiv.0710.1283
To appear in Ergodic Theory Dynam. Systems
arxiv created 2007/10/05 · openalex publication_date 2007/10/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove the following renewal-type limit theorem. Given an irrational α in (0,1) 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.