Renewal-type Limit Theorem for the Gauss Map and Continued Fractions
| dc.creator | Sinai, Yakov G. | |
| dc.creator | Ulcigrai, Corinna | |
| dc.date | 2007-10-05 | |
| dc.date.accessioned | 2026-07-07T08:34:27Z | |
| dc.date.available | 2026-07-07T08:34:27Z | |
| dc.description | In 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.description | To appear in Ergodic Theory Dynam. Systems | |
| dc.identifier | https://arxiv.org/abs/0710.1283 | |
| dc.identifier | http://arxiv.org/abs/0710.1283 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139441 | |
| dc.subject | Dynamical Systems | |
| dc.title | Renewal-type Limit Theorem for the Gauss Map and Continued Fractions | |
| dc.type | text |