The Oppenheim series expansions and Hausdorff dimensions
Jun Wu (2003)
Acta Arithmetica
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Jun Wu (2003)
Acta Arithmetica
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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.
Yan-Yan Liu, Jun Wu (2001)
Acta Arithmetica
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Bao-Wei Wang, Jun Wu (2006)
Acta Arithmetica
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Lu-ming Shen (2010)
Acta Arithmetica
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Frank Terpe (1971)
Colloquium Mathematicae
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J. W. Bebernes, Steven K. Ingram (1971)
Annales Polonici Mathematici
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M. A. Selby (1974)
Colloquium Mathematicae
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D. Ž. Đoković (1968)
Publications de l'Institut Mathématique
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A. M. Stokolos (2006)
Colloquium Mathematicae
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The study of one-dimensional rare maximal functions was started in [4,5]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we call it "dyadic crystallization") to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function.
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.
Doroslovački, Rade, Pantović, Jovanka, Vojvodić, Gradimir (1999)
Novi Sad Journal of Mathematics
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T. Radul (2006)
Colloquium Mathematicae
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We prove the addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial.
Haddad, Lucien, Lau, Dietlinde (2000)
Beiträge zur Algebra und Geometrie
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Takahisa Miyata, Žiga Virk (2013)
Fundamenta Mathematicae
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Hurewicz's dimension-raising theorem states that dim Y ≤ dim X + n for every n-to-1 map f: X → Y. In this paper we introduce a new notion of finite-to-one like map in a large scale setting. Using this notion we formulate a dimension-raising type theorem for asymptotic dimension and asymptotic Assouad-Nagata dimension. It is also well-known (Hurewicz's finite-to-one mapping theorem) that dim X ≤ n if and only if there exists an (n+1)-to-1 map from a 0-dimensional space onto X. We formulate...
Veerman, J.J.P., Stošić, B.D. (2000)
Experimental Mathematics
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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.
Jaroslav Hančl, Radhakrishnan Nair, Lukáš Novotný, Jan Šustek (2012)
Acta Arithmetica
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Carlo Sbordone, Ingemar Wik (1994)
Publicacions Matemàtiques
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The famous result of Muckenhoupt on the connection between weights w in A-classes and the boundedness of the maximal operator in L(w) is extended to the case p = ∞ by the introduction of the geometrical maximal operator. Estimates of the norm of the maximal operators are given in terms of the A-constants. The equality of two differently defined A-constants is proved. Thereby an answer is given to a question posed by R. Johnson. For non-increasing functions on the positive real line a...
Kazuhiro Kawamura, Kazuo Tomoyasu (2001)
Colloquium Mathematicae
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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).