Contracting-on-Average Baker Maps
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.
Displaying similar documents to “Separation conditions on controlled Moran constructions”
Contracting-on-Average Baker Maps
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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Semicontinuity of dimension and measure for locally scaling fractals
L. B. Jonker, J. J. P. Veerman (2002)
Fundamenta Mathematicae
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The basic question of this paper is: If you consider two iterated function systems close to each other in an appropriate topology, are the dimensions of their respective invariant sets close to each other? It is well known that the Hausdorff dimension (and Lebesgue measure) of the invariant set does not depend continuously on the iterated function system. Our main result is that (with a restriction on the "non-conformality" of the transformations) the Hausdorff dimension is a lower semicontinuous...
Collectionwise Hausdorff property in product spaces
T. Przymusiński (1976)
Colloquium Mathematicae
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Two counterexamples concerning Hausdorff dimensions of projections
Roy O. Davies (1979)
Colloquium Mathematicae
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Hausdorff spaces and the closed intersection property
D. W. Hajek (1982)
Matematički Vesnik
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On Nikodym-type sets in high dimensions
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.
On the Hausdorff dimension of a family of self-similar sets with complicated overlaps
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...
A further discussion of the Hausdorff dimension in Engel expansions
Lu-ming Shen (2010)
Acta Arithmetica
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On the Hausdorff dimension of ultrametric subsets in ℝⁿ
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).
Hausdorff Measure of Infinitely Generated Self-Similar Sets.
M. Moran (1996)
Monatshefte für Mathematik
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On the Hausdorff dimension of the expressible set of certain sequences
Jaroslav Hančl, Radhakrishnan Nair, Lukáš Novotný, Jan Šustek (2012)
Acta Arithmetica
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Generic Properties of Continuous Iterated Function Systems with Place Dependent Probabilities
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.
On some properties of Hausdorff content related to instability.
Mattila, Pertti, Orobitg, Joan (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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On the dimensions of certain incommensurably constructed sets.
Veerman, J.J.P., Stošić, B.D. (2000)
Experimental Mathematics
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On the dimension of an irrigable measure
Giuseppe Devillanova, Sergio Solimini (2007)
Rendiconti del Seminario Matematico della Università di Padova
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Hausdorff dimensions in Engel expansions
Yan-Yan Liu, Jun Wu (2001)
Acta Arithmetica
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Khinchin's theorem in k dimensions with prime numerator and denominator
Huw Jones (2001)
Acta Arithmetica
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Infinite Iterated Function Systems: A Multivalued Approach
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.