A further discussion of the Hausdorff dimension in Engel expansions
Lu-ming Shen (2010)
Acta Arithmetica
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Lu-ming Shen (2010)
Acta Arithmetica
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Veerman, J.J.P., Stošić, B.D. (2000)
Experimental Mathematics
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Jaroslav Hančl, Radhakrishnan Nair, Lukáš Novotný, Jan Šustek (2012)
Acta Arithmetica
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Balázs Bárány (2009)
Fundamenta Mathematicae
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We investigate the properties of the Hausdorff dimension of the attractor of the iterated function system (IFS) {γx,λx,λx+1}. Since two maps have the same fixed point, there are very complicated overlaps, and it is not possible to directly apply known techniques. We give a formula for the Hausdorff dimension of the attractor for Lebesgue almost all parameters (γ,λ), γ < λ. This result only holds for almost all parameters: we find a dense set of parameters (γ,λ) for which the Hausdorff...
James R. Lee, Manor Mendel, Mohammad Moharrami (2012)
Fundamenta Mathematicae
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For every ε > 0, any subset of ℝⁿ with Hausdorff dimension larger than (1-ε)n must have ultrametric distortion larger than 1/(4ε).
Yan-Yan Liu, Jun Wu (2001)
Acta Arithmetica
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Themis Mitsis (2004)
Studia Mathematica
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We prove that the complement of a higher-dimensional Nikodym set must have full Hausdorff dimension.
T. W. Körner (2008)
Studia Mathematica
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There is no non-trivial constraint on the Hausdorff dimension of sums of a set with itself.
T. Przymusiński (1976)
Colloquium Mathematicae
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D. W. Hajek (1982)
Matematički Vesnik
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Guifeng Huang, Lidong Wang (2014)
Annales Polonici Mathematici
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A solution of the Feigenbaum functional equation is called a Feigenbaum map. We investigate the likely limit set (i.e. the maximal attractor in the sense of Milnor) of a non-unimodal Feigenbaum map, prove that it is a minimal set that attracts almost all points, and then estimate its Hausdorff dimension. Finally, for every s ∈ (0,1), we construct a non-unimodal Feigenbaum map with a likely limit set whose Hausdorff dimension is s.
Satya Deo, Subhash Muttepawar (1988)
Colloquium Mathematicae
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Quansheng Liu (1993)
Publications mathématiques et informatique de Rennes
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Mattila, Pertti, Orobitg, Joan (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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F. Przytycki, M. Urbański (1989)
Studia Mathematica
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W. Kulpa (1972)
Colloquium Mathematicae
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Jun Wu (2003)
Acta Arithmetica
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Igudesman, K. (2003)
Lobachevskii Journal of Mathematics
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Jianmiao Ruan, Dashan Fan, Hongliang Li (2020)
Czechoslovak Mathematical Journal
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We study the high-dimensional Hausdorff operators on the Morrey space and on the Campanato space. We establish their sharp boundedness on these spaces. Particularly, our results solve an open question posted by E. Liflyand (2013).
R. Duda (1979)
Colloquium Mathematicae
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Ondřej Zindulka (2012)
Fundamenta Mathematicae
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We prove that each analytic set in ℝⁿ contains a universally null set of the same Hausdorff dimension and that each metric space contains a universally null set of Hausdorff dimension no less than the topological dimension of the space. Similar results also hold for universally meager sets. An essential part of the construction involves an analysis of Lipschitz-like mappings of separable metric spaces onto Cantor cubes and self-similar sets.