Hausdorff dimensions in Engel expansions
Yan-Yan Liu, Jun Wu (2001)
Acta Arithmetica
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Yan-Yan Liu, Jun Wu (2001)
Acta Arithmetica
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Lu-ming Shen (2010)
Acta Arithmetica
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Jaroslav Hančl, Radhakrishnan Nair, Lukáš Novotný, Jan Šustek (2012)
Acta Arithmetica
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Veerman, J.J.P., Stošić, B.D. (2000)
Experimental Mathematics
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Simon Baker (2012)
Fundamenta Mathematicae
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In a recent paper of Feng and Sidorov they show that for β ∈ (1,(1+√5)/2) the set of β-expansions grows exponentially for every x ∈ (0,1/(β-1)). In this paper we study this growth rate further. We also consider the set of β-expansions from a dimension theory perspective.
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).
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...
T. Przymusiński (1976)
Colloquium Mathematicae
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D. W. Hajek (1982)
Matematički Vesnik
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Mattila, Pertti, Orobitg, Joan (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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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.
Eda Cesaratto, Brigitte Vallée (2006)
Acta Arithmetica
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Satya Deo, Subhash Muttepawar (1988)
Colloquium Mathematicae
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Yu Sun, Jian Xu (2018)
Czechoslovak Mathematical Journal
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We obtain a metrical property on the asymptotic behaviour of the maximal run-length function in the Lüroth expansion. We also determine the Hausdorff dimension of a class of exceptional sets of points whose maximal run-length function has sub-linear growth rate.
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.
Piotr Borodulin-Nadzieja, David Chodounský (2015)
Fundamenta Mathematicae
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We define and study two classes of uncountable ⊆*-chains: Hausdorff towers and Suslin towers. We discuss their existence in various models of set theory. Some of the results and methods are used to provide examples of indestructible gaps not equivalent to a Hausdorff gap. We also indicate possible ways of developing a structure theory for towers based on classification of their Tukey types.
Bao-Wei Wang, Jun Wu (2006)
Acta Arithmetica
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Igudesman, K. (2003)
Lobachevskii Journal of Mathematics
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F. Przytycki, M. Urbański (1989)
Studia Mathematica
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Quansheng Liu (1993)
Publications mathématiques et informatique de Rennes
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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).