On the dimensions of certain incommensurably constructed sets.
Veerman, J.J.P., Stošić, B.D. (2000)
Experimental Mathematics
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Veerman, J.J.P., Stošić, B.D. (2000)
Experimental Mathematics
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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).
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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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. 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.
Yan-Yan Liu, Jun Wu (2001)
Acta Arithmetica
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Satya Deo, Subhash Muttepawar (1988)
Colloquium Mathematicae
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Quansheng Liu (1993)
Publications mathématiques et informatique de Rennes
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T. Przymusiński (1976)
Colloquium Mathematicae
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W. Kulpa (1972)
Colloquium Mathematicae
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Eda Cesaratto, Brigitte Vallée (2006)
Acta Arithmetica
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Antti Käenmäki, Markku Vilppolainen (2008)
Fundamenta Mathematicae
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It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.
D. W. Hajek (1982)
Matematički Vesnik
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Józef Myjak, Ryszard Rudnicki (2007)
Bollettino dell'Unione Matematica Italiana
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A relationship between the information dimension and the average dimension of a measure is given. Properties of the average dimension are studied.
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.
Mattila, Pertti, Orobitg, Joan (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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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.
Balázs Bárány (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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We investigate properties of the zero of the subadditive pressure which is a most important tool to estimate the Hausdorff dimension of the attractor of a non-conformal iterated function system (IFS). Our result is a generalization of the main results of Miao and Falconer [Fractals 15 (2007)] and Manning and Simon [Nonlinearity 20 (2007)].
F. Przytycki, M. Urbański (1989)
Studia Mathematica
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Michał Rams (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We estimate from above and below the Hausdorff dimension of SRB measure for contracting-on-average baker maps.
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. ...
Edoardo Vesentini (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Si dimostra con esempi che la distanza di Hausdorff-Carathéodory fra i valori di funzioni multivoche, analitiche secondo Oka, non è subarmonica.
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.
Jonathan M. Fraser (2012)
Studia Mathematica
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We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some results of Olsen and Snigireva by computing the upper box dimensions assuming some mild separation conditions. Secondly, we investigate the more difficult problem of computing the lower box dimension. We give some non-trivial bounds and provide examples to show that lower box dimension behaves much more strangely than upper box dimension, Hausdorff dimension and packing dimension.