On the dimensions of a family of overlapping self-affine carpets

Jonathan M. Fraser, Pablo Shmerkin

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish
    Pages (from-to)2463-2481
    Number of pages19
    JournalErgodic Theory and Dynamical Systems
    Issue number8
    Early online date21 Jul 2015
    Publication statusPublished - 1 Dec 2016


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