### 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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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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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...

Jun Wu (2003)

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. Przymusiński (1976)

Colloquium Mathematicae

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Satya Deo, Subhash Muttepawar (1988)

Colloquium Mathematicae

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D. W. Hajek (1982)

Matematički Vesnik

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Quansheng Liu (1993)

Publications mathématiques et informatique de Rennes

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Eda Cesaratto, Brigitte Vallée (2006)

Acta Arithmetica

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W. Kulpa (1972)

Colloquium Mathematicae

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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.

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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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.

Igudesman, K. (2003)

Lobachevskii Journal of Mathematics

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R. Duda (1979)

Colloquium Mathematicae

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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.

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.

Yves Dutrieux, Nigel J. Kalton (2005)

Studia Mathematica

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We study the Gromov-Hausdorff and Kadets distances between C(K)-spaces and their quotients. We prove that if the Gromov-Hausdorff distance between C(K) and C(L) is less than 1/16 then K and L are homeomorphic. If the Kadets distance is less than one, and K and L are metrizable, then C(K) and C(L) are linearly isomorphic. For K and L countable, if C(L) has a subquotient which is close enough to C(K) in the Gromov-Hausdorff sense then K is homeomorphic to a clopen subset of L. ...