A Limit Theorem for Birkoff sums of non-integrable functions over rotations
| dc.creator | Sinai, Yakov G. | |
| dc.creator | Ulcigrai, Corinna | |
| dc.date | 2007-10-05 | |
| dc.date | 2008-06-24 | |
| dc.date.accessioned | 2026-07-07T09:45:58Z | |
| dc.date.available | 2026-07-07T09:45:58Z | |
| dc.description | We consider Birkhoff sums of functions with a singularity of type 1/x over rotations and prove the following limit theorem. Let $S_N= S_N(α,x)$ be the N^th non-renormalized Birkhoff sum, where $x in [0,1)$ is the initial point, $α\in [0,1)$ is the rotation number and $(α, x)$ are uniformly distributed. We prove that $S_N/N$ has a joint limiting distribution in $(α,x)$ as N tends to infinity. As a corollary, we get the existence of a limiting distribution for certain trigonometric sums. | |
| dc.description | 24 pages, some typos corrected, final version to appear in ``Probabilistic and Geometric Structures in Dynamics'', edited by K. Burns, D. Dolgopyat, and Ya. Pesis, American Mathematical Society, Contemporary Mathematics Series | |
| dc.identifier | https://arxiv.org/abs/0710.1287 | |
| dc.identifier | http://arxiv.org/abs/0710.1287 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163373 | |
| dc.subject | Dynamical Systems | |
| dc.title | A Limit Theorem for Birkoff sums of non-integrable functions over rotations | |
| dc.type | text |