Invariant sets with zero measure and full Hausdorff dimension.
Barreira, Luis, Schmeling, Jörg (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Barreira, Luis, Schmeling, Jörg (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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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.
Veerman, J.J.P., Stošić, B.D. (2000)
Experimental Mathematics
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Franz Hofbauer, Peter Raith, Thomas Steinberger (2003)
Fundamenta Mathematicae
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The multifractal generalizations of Hausdorff dimension and packing dimension are investigated for an invariant subset A of a piecewise monotonic map on the interval. Formulae for the multifractal dimension of an ergodic invariant measure, the essential multifractal dimension of A, and the multifractal Hausdorff dimension of A are derived.
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.
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...
Paweł Góra (1989)
Banach Center Publications
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Lu-ming Shen (2010)
Acta Arithmetica
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Giuseppe Devillanova, Sergio Solimini (2007)
Rendiconti del Seminario Matematico della Università di Padova
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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).
Jaroslav Hančl, Radhakrishnan Nair, Lukáš Novotný, Jan Šustek (2012)
Acta Arithmetica
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Tomasz Bielaczyc (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is shown that for a typical continuous learning system defined on a compact convex subset of ℝⁿ the Hausdorff dimension of its invariant measure is equal to zero.
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.
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.
R. Đorđević (1989)
Matematički Vesnik
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Franz Hofbauer (1996)
Monatshefte für Mathematik
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Tomasz Bielaczyc (2011)
Annales Polonici Mathematici
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It is shown that the Hausdorff dimension of an invariant measure generated by a Poisson driven stochastic differential equation is greater than or equal to 1.
Antoni Leon Dawidowicz (1992)
Annales Polonici Mathematici
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A generalization of the Avez method of construction of an invariant measure is presented.
Huw Jones (2001)
Acta Arithmetica
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K. Leśniak (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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We prove that a compact family of bounded condensing multifunctions has bounded condensing set-theoretic union. Compactness is understood in the sense of the Chebyshev uniform semimetric induced by the Hausdorff distance and condensity is taken w.r.t. the Hausdorff measure of noncompactness. As a tool, we present an estimate for the measure of an infinite union. Then we apply our result to infinite iterated function systems.
Satya Deo, Subhash Muttepawar (1988)
Colloquium Mathematicae
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Yan-Yan Liu, Jun Wu (2001)
Acta Arithmetica
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Myjak, Józef (2005)
Abstract and Applied Analysis
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