2 1 Ju n 20 12 DIMENSIONS OF SOME FRACTALS DEFINED VIA THE SEMIGROUP GENERATED
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
Dimensions of Some Fractals Defined via the Semigroup
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.
متن کامل. D S ] 2 9 Ju n 20 05 Dimensions of Julia sets of expanding rational semigroups ∗
We estimate the upper box and Hausdorff dimensions of the Julia set of an expanding semigroup generated by finitely many rational functions, using the thermodynamic formalism in ergodic theory. Furthermore, we show Bowen’s formula, and the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition.
متن کاملm at h . D S ] 1 0 Ju n 20 05 Dimensions of Julia sets of expanding rational semigroups ∗
We estimate the upper box and Hausdorff dimensions of the Julia set of an expanding semigroup generated by finitely many rational functions, using the thermodynamic formalism in ergodic theory. Furthermore, we show Bowen’s formula, and the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition.
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The Cuntz semigroup is computed for spaces X of dimension at most 2 such thatˇH 2 (X, Z) = 0. This computation is then extended to spaces of dimension at most 2 such thatˇH 2 (X\{x}, Z) = 0 for all x ∈ X (e.g., any compact surface). It is also shown that for these two classes of spaces the Cuntz equivalence of countably generated Hilbert C*-modules (over C 0 (X)) amounts to their isomorphism.
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