Dimensions of Some Fractals Defined via the Semigroup
نویسنده
چکیده
We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Σm = {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.
منابع مشابه
2 1 Ju n 20 12 DIMENSIONS OF SOME FRACTALS DEFINED VIA THE SEMIGROUP GENERATED
We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Σm = {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.
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