On the dimensions of a family of overlapping self-affine carpets
On the dimensions of a family of overlapping self-affine carpets
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DOI：
10.1017/etds.2015.21
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发表时间：
2014-05
影响因子：
0.9
通讯作者：
J. Fraser;Pablo Shmerkin
中科院分区：
文献类型：
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作者：
J. Fraser;Pablo Shmerkin
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 randomize 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, Hochman’s recent work on the dimensions of self-similar sets and measures.
