The probability distribution and Hausdorff dimension of self-affine functions

DOI10.1007/BF01197891zbMath0688.60012MaRDI QIDQ1263862

Mariusz Urbański

Publication date: 1990

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

Hausdorff dimensioncontinuous self-affine functionnecessary and sufficient condition for this distribution to be absolutely continuous with respect to Lebesgue measure

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Continuity and singularity of induced measures (60G30)

Related Items (8)

A variational formula for dimension spectra of linear cellular automata ⋮ A dimension formula for Bernoulli convolutions ⋮ Hausdorff dimensions of sofic affine-invariant sets ⋮ Fractional Differentiation in the Self‐Affine Case. V ‐ The Local Degree of Differentiability ⋮ Measures of Full Dimension on Self-Affine Graphs ⋮ Convergence of complex multiplicative cascades ⋮ The \(n\)-dimensional Peano curve ⋮ The box and Hausdorff dimension of self-affine sets

Cites Work

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• The metric entropy of diffeomorphisms. II: Relations between entropy, exponents and dimension
• On the Hausdorff dimension of some fractal sets
• Dimension, entropy and Lyapunov exponents
• On self-affine functions
• A characterization of self-affine functions
• Invariant subsets of expanding mappings of the circle
• On self-affine functions II
• The box and Hausdorff dimension of self-affine sets

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