Files in this item
On the dimensions of a family of overlapping self-affine carpets
Item metadata
dc.contributor.author | Fraser, Jonathan MacDonald | |
dc.contributor.author | Shmerkin, Pablo | |
dc.date.accessioned | 2016-11-17T12:30:19Z | |
dc.date.available | 2016-11-17T12:30:19Z | |
dc.date.issued | 2016-12 | |
dc.identifier | 247731017 | |
dc.identifier | eac5a415-953e-41d9-a42d-d0534665fe17 | |
dc.identifier | 84937598501 | |
dc.identifier.citation | Fraser , J M & Shmerkin , P 2016 , ' On the dimensions of a family of overlapping self-affine carpets ' , Ergodic Theory and Dynamical Systems , vol. 36 , no. 8 , pp. 2463–2481 . https://doi.org/10.1017/etds.2015.21 | en |
dc.identifier.issn | 0143-3857 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/58285488 | |
dc.identifier.uri | https://hdl.handle.net/10023/9835 | |
dc.description | The work of J.M.F. was supported by the EPSRC grant EP/J013560/1 whilst at Warwick and an EPSRC doctoral training grant whilst at St Andrews. | en |
dc.description.abstract | 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. | |
dc.format.extent | 482394 | |
dc.language.iso | eng | |
dc.relation.ispartof | Ergodic Theory and Dynamical Systems | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | On the dimensions of a family of overlapping self-affine carpets | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1017/etds.2015.21 | |
dc.description.status | Peer reviewed | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.