On the dimensions of a family of overlapping self-affine carpets
We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translation vectors with the stipulation that the column structure is preserved. As such, we maintain one of the key features in...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2016 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/53255 |
| Online Access: | http://hdl.handle.net/11336/53255 |
| Access Level: | Open access |
| Keyword: | SELF-AFFINE CARPET HAUSDORFF DIMENSION PACKING DIMENSION BOX DIMENSION OVERLAPS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translation vectors with the stipulation that the column structure is preserved. As such, we maintain one of the key features in the Bedford-McMullen set up in that alignment causes the dimensions to drop from the affinity dimension. We compute the Hausdorff, packing and box dimensions outside of a small set of exceptional translations, and also for some explicit translations even in the presence of overlapping. Our results rely on, and can be seen as a partial extension of, M. Hochman´s recent work on the dimensions of self-similar sets and measures. |
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