Renewal-type Limit Theorem for the Gauss Map and Continued Fractions

dc.creatorSinai, Yakov G.
dc.creatorUlcigrai, Corinna
dc.date2007-10-05
dc.date.accessioned2026-07-07T08:34:27Z
dc.date.available2026-07-07T08:34:27Z
dc.descriptionIn this paper we prove the following renewal-type limit theorem. Given an irrational $α$ in (0,1) and R>0, let $q_{n_R}$ be the first denominator of the convergents of $α$ which exceeds R. The main result in the paper is that the ratio $q_{n_R}/R$ 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.
dc.descriptionTo appear in Ergodic Theory Dynam. Systems
dc.identifierhttps://arxiv.org/abs/0710.1283
dc.identifierhttp://arxiv.org/abs/0710.1283
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139441
dc.subjectDynamical Systems
dc.titleRenewal-type Limit Theorem for the Gauss Map and Continued Fractions
dc.typetext

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