Self-similar and self-affine sets; measure of the intersection of two copies
| dc.creator | Elekes, Márton | |
| dc.creator | Keleti, Tamás | |
| dc.creator | Máthé, András | |
| dc.date | 2007-04-27 | |
| dc.date | 2008-07-14 | |
| dc.date.accessioned | 2026-07-07T09:49:44Z | |
| dc.date.available | 2026-07-07T09:49:44Z | |
| dc.description | Let K be a self-similar or self-affine set in R^d, let μbe a self-similar or self-affine measure on it, and let G be the group of affine maps, similitudes, isometries or translations of R^d. Under various assumptions (such as separation conditions or we assume that the transformations are small perturbations or that K is a so called Sierpinski sponge) we prove theorems of the following types, which are closely related to each other; Non-stability: There exists a constant c<1 such that for every g\in G we have either μ(K\cap g(K)) <c μ(K) or K\subset g(K). Measure and topology: For every g\in G we have μ(K\cap g(K)) > 0 \iff int_K (K\cap g(K)) is nonempty (where int_K is interior relative to K). Extension: The measure μhas a G-invariant extension to R^d. Moreover, in many situations we characterize those g's for which μ(K\cap g(K) > 0, and we also get results about those $g$'s for which $g(K)\su K$ or $g(K)\supset K$ holds. | |
| dc.identifier | https://arxiv.org/abs/0704.3727 | |
| dc.identifier | http://arxiv.org/abs/0704.3727 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164700 | |
| dc.subject | General Mathematics | |
| dc.subject | 28A80; 28C10 | |
| dc.title | Self-similar and self-affine sets; measure of the intersection of two copies | |
| dc.type | text |