Displaying similar documents to “Contracting-on-Average Baker Maps”

Separation conditions on controlled Moran constructions

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.

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...

On the Information Dimensions

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.

On the attractors of Feigenbaum maps

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.

Subadditive Pressure for IFS with Triangular Maps

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)].

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...

On the Relations Between 2D and 3D Fractal Dimensions: Theoretical Approach and Clinical Application in Bone Imaging

H. Akkari, I. Bhouri, P. Dubois, M. H. Bedoui (2008)

Mathematical Modelling of Natural Phenomena

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The inner knowledge of volumes from images is an ancient problem. This question becomes complicated when it concerns quantization, as the case of any measurement and in particular the calculation of fractal dimensions. Trabecular bone tissues have, like many natural elements, an architecture which shows a fractal aspect. Many studies have already been developed according to this approach. The question which arises however is to know to which extent it is possible to get an exact determination...

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.

Completely mixing maps without limit measure

Gerhard Keller (2004)

Colloquium Mathematicae

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We combine some results from the literature to give examples of completely mixing interval maps without limit measure.