Dimensions Of Some Fractals Defined Via The Semigroup Generated By 2 And 3

  • Yuval Peres ,
  • Joerg Schmeling ,
  • Stéphane Seuret ,
  • Boris Solomyak

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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∈Σm:∀k, xkx2k...xnk=0}, where n≥3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.