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

Yuval Peres, Jörg Schmeling, Stephane Seuret, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

Abstract

We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Sigma(m) ={0, ... , m-1}(N) that are invariant under multiplication by integers. The results apply to the sets {x is an element of Sigma(m): for all k, x(k)x(2k) ... x(nk) = 0}, where n >= 3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.
Original languageEnglish
Pages (from-to)687-709
JournalIsrael Journal of Mathematics
Volume199
Issue number2
DOIs
Publication statusPublished - 2014

Subject classification (UKÄ)

  • Mathematics

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