Dilatation structures II. Linearity, self-similarity and the Cantor set
| dc.creator | Buliga, Marius | |
| dc.date | 2006-12-18 | |
| dc.date | 2007-02-14 | |
| dc.date.accessioned | 2026-07-07T07:46:38Z | |
| dc.date.available | 2026-07-07T07:46:38Z | |
| dc.description | In this paper we continue the study of dilatation structures, introduced in math.MG/0608536 . A dilatation structure on a metric space is a kind of enhanced self-similarity. By way of examples this is explained here with the help of the middle-thirds Cantor set. Linear and self-similar dilatation structures are introduced and studied on ultrametric spaces, especially on the boundary of the dyadic tree (same as the middle-thirds Cantor set). Some other examples of dilatation structures, which share some common features, are given. Another class of examples, coming from sub-Riemannian geometry, will make the subject of an article in preparation. In the particular case of ultrametric spaces the axioms of dilatation structures take a simplified form, leading to a description of all possible weak dilatation structures on the Cantor set. As an application we prove that there is more than one linear and self-similar dilatation structure on the Cantor set, compatible with the iterated functions system which defines the Cantor set. Applications to self-similar groups are reserved for a further paper. | |
| dc.identifier | https://arxiv.org/abs/math/0612509 | |
| dc.identifier | http://arxiv.org/abs/math/0612509 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123890 | |
| dc.subject | Metric Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 20F65; 22A10; 51F99 | |
| dc.title | Dilatation structures II. Linearity, self-similarity and the Cantor set | |
| dc.type | text |