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Article Dans Une Revue Israel Journal of Mathematics Année : 2014

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

Résumé

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 $\{x\in \Sigma_m: \forall\, k, \ x_k x_{2k}... x_{n k}=0\}$, where $n\ge 3$. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.

Dates et versions

hal-00795615 , version 1 (28-02-2013)

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Yuval Peres, Joerg Schmeling, Stéphane Seuret, Boris Solomyak. Dimensions of some fractals defined via the semigroup generated by 2 and 3. Israel Journal of Mathematics, 2014, 199 (2), pp.687-709. ⟨10.1007/s11856-013-0058-z⟩. ⟨hal-00795615⟩
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