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

Yuval Peres; Joerg Schmeling; Stéphane Seuret; Boris Solomyak

doi:10.1007/s11856-013-0058-z

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 journal › Article › peer-review

21 Scopus citations

Abstract

We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Σ_m={0,..,m−1}^ℕ that are invariant under multiplication by integers. The results apply to the sets {x∈Σ_m:∀ k, x_kx_2k.. x_nk =0}, where n ≥ 3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.

Original language	English
Pages (from-to)	687-709
Number of pages	23
Journal	Israel Journal of Mathematics
Volume	199
Issue number	2
DOIs	https://doi.org/10.1007/s11856-013-0058-z
State	Published - 1 Mar 2014
Externally published	Yes

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Publisher Copyright:
© 2014, Hebrew University Magnes Press.

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

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