A note on the dimension Dind
W. Kulpa (1972)
Colloquium Mathematicae
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W. Kulpa (1972)
Colloquium Mathematicae
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R. Duda (1979)
Colloquium Mathematicae
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R. Đorđević (1989)
Matematički Vesnik
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Veerman, J.J.P., Stošić, B.D. (2000)
Experimental Mathematics
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L. Polkowski (1985)
Colloquium Mathematicae
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Juan B. Sancho de Salas, M.ª Teresa Sancho de Salas (1988)
Extracta Mathematicae
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Lu-ming Shen (2010)
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).
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.
Weber, Hermann-Josef (1997)
Experimental Mathematics
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Jaroslav Hančl, Radhakrishnan Nair, Lukáš Novotný, Jan Šustek (2012)
Acta Arithmetica
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Satya Deo, Subhash Muttepawar (1988)
Colloquium Mathematicae
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Herrmann Haase (1988)
Acta Universitatis Carolinae. Mathematica et Physica
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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...