Further Baire results on the distribution of subsequences
| dc.creator | Goldstern, Martin | |
| dc.creator | Schmeling, Jörg | |
| dc.creator | Winkler, Reinhard | |
| dc.date | 2004-07-16 | |
| dc.date | 2007-11-22 | |
| dc.date.accessioned | 2026-07-07T08:44:19Z | |
| dc.date.available | 2026-07-07T08:44:19Z | |
| dc.description | This paper presents results about the distribution of subsequences which are typical in the sense of Baire. The first part is concerned with sequences of the type x_k = n_k*alpha, n_1 < n_2 < n_3 < ..., mod 1. Improving a result of Salat we show that, if the quotients q_k = n_{k+1}/n_k satisfy q_k > 1+ epsilon, then the set of alpha such that (x_k) is uniformly distributed is of first Baire category, i.e. for generic alpha we do not have uniform distribution. Under the stronger assumption lim q_k = infinity one even has maldistribution for generic alpha, the strongest possible contrast to uniform distribution. The second part reverses the point of view by considering appropriately defined Baire spaces S of subsequences. For a fixed well distributed sequence (x_n) we show that there is a set M of measures such that for generic (n_k) in S the set of limit measures of the subsequence (x_{n_k}) is exactly M. | |
| dc.description | 21 pages, LaTeX2e. Final version. (Somewhat expanded proofs and clarifications, more examples) | |
| dc.identifier | https://arxiv.org/abs/math/0407295 | |
| dc.identifier | http://arxiv.org/abs/math/0407295 | |
| dc.identifier | Uniform Distribution Theory 2 (2007), no. 1, 127-149 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142615 | |
| dc.subject | Number Theory | |
| dc.subject | Dynamical Systems | |
| dc.subject | 11K06 (Primary), 37A45 (Secondary) | |
| dc.title | Further Baire results on the distribution of subsequences | |
| dc.type | text |