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On Hausdorff Dimension of Unimodal Attractors
Communications in Mathematical Physics, 2006The paper deals with the \(C^4\) unimodal maps \(f: I\to I\), where \(I\) is a compact interval and \(f\) maps the boundary of \(I\) into itself. Further is supposed that the critical point \(\xi\) of \(f\) \((f'(\xi)= 0)\) belongs to the interior of \(I\) and is nondegenerate \((f''(\xi)\neq 0)\). The authors prove the following result: There exists a
Graczyk, J., Kozlovski, O. S.
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HAUSDORFF DIMENSION OF A FAMILY OF NETWORKS
Fractals, 2023For a family of networks [Formula: see text], we define the Hausdorff dimension of [Formula: see text] inspired by the Frostman’s characteristics of potential for Hausdorff dimension of fractals on Euclidean spaces. We prove that our Hausdorff dimension of the touching networks is [Formula: see text] Our definition is quite different from the fractal ...
QINGCHENG ZENG, LIFENG XI
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ON HAUSDORFF DIMENSION AND TOPOLOGICAL ENTROPY
Fractals, 2010Let f: X → X be a continuous map of a compact topological space. If there exists a metric function on X and it satisfies some restricted conditions, we obtain some relationships between Hausdorff dimension and topological entropy for any Z ⊆ X. Using those results, we also obtain a variational principle of dimensions, generalize some known results and
Ma, Dongkui, Wu, Min
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On Estimations of the Generalized Hausdorff Dimension
Vestnik St. Petersburg University, Mathematics, 2019The authors introduce the abstract concept of a homogeneous dimensional space and associate with such spaces a finite compactness index. Additionally, they define a Hausdorff-Besicovitch dimension spectrum and prove a theorem about the values of the Hausdorff-Besicovitch dimension spectrum for subspaces of homogenous dimensional spaces.
Leonov, G. A., Florinskii, A. A.
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Hausdorff dimension in exponential time
Proceedings 16th Annual IEEE Conference on Computational Complexity, 2002In this paper we investigate effective versions of Hausdorff dimension which have been recently introduced by Lutz. We focus on dimension in the class E of sets computable in linear exponential time. We determine the dimension of various classes related to fundamental structural properties including different types of autoreducibility and immunity.
Klaus Ambos-Spies +3 more
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Subcomputable Hausdorff function dimension
Theoretical Computer Science, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Hausdorff Dimension versus Smoothness
2007There is a one-to-one correspondence between C1+H Cantor exchange systems that are C1+H fixed points of renormalization and C1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, there is no such C1+α Cantor exchange system
Ferreira, Flávio +2 more
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Hausdorff dimension of univoque sets
Acta Cybern., 1999Summary: We present the results obtained so far for the determination of the Hausdorff dimension of the univoque set in number systems with base number greater than 1. The investigation is based on the methods presented in \textit{Z. Daróczy} and \textit{I. Kátai} [Publ. Math. 42, 397-407 (1993; Zbl 0809.11008) and ibid.
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