Dimensions of some fractals defined via the semigroup generated by 2 and 3

Yuval Peres, Joerg Schmeling, Stéphane Seuret, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Σm={0,..,m−1} that are invariant under multiplication by integers. The results apply to the sets {x∈Σm:∀ k, xkx2k.. xnk =0}, where n ≥ 3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.

Original languageEnglish
Pages (from-to)687-709
Number of pages23
JournalIsrael Journal of Mathematics
Volume199
Issue number2
DOIs
StatePublished - 1 Mar 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014, Hebrew University Magnes Press.

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