Purely periodic beta-expansions in the Pisot non-unit case
| dc.creator | Berthe, Valerie | |
| dc.creator | Siegel, Anne | |
| dc.date | 2004-07-15 | |
| dc.date.accessioned | 2026-07-07T05:10:23Z | |
| dc.date.available | 2026-07-07T05:10:23Z | |
| dc.description | It is well known that real numbers with a purely periodic decimal expansion are the rationals having, when reduced, a denominator coprime with 10. The aim of this paper is to extend this result to beta-expansions with a Pisot base beta which is not necessarily a unit: we characterize real numbers having a purely periodic expansion in such a base; this characterization is given in terms of an explicit set, called generalized Rauzy fractal, which is shown to be a graph-directed self-affine compact subset of non-zero measure which belongs to the direct product of Euclidean and p-adic spaces. | |
| dc.identifier | https://arxiv.org/abs/math/0407282 | |
| dc.identifier | http://arxiv.org/abs/math/0407282 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71912 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Primary 37B10; Secondary 11R06, 11A63, 11J70, 68R15 | |
| dc.title | Purely periodic beta-expansions in the Pisot non-unit case | |
| dc.type | text |