Multifractal structure of Bernoulli convolutions

DOI10.1017/S0305004111000466zbMath1248.11054arXiv1011.1938MaRDI QIDQ3095782

Pablo Shmerkin, Thomas M. Jordan, B. M. Solomyak

Publication date: 4 November 2011

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.1938

zbMATH Keywords

multifractal analysisBernoulli convolutions\(\beta\)-transformationsfractals with overlaprandom self-similar multifractals

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80) Hausdorff and packing measures (28A78) Dimension theory of smooth dynamical systems (37C45)

Related Items (21)

Random Lochs’ Theorem ⋮ Recent progress on Bernoulli convolutions ⋮ The infinite derivatives of Okamoto's self-affine functions: an application of \(\beta\)-expansions ⋮ Differentiability of a two-parameter family of self-affine functions ⋮ Finite orbits in multivalued maps and Bernoulli convolutions ⋮ Multifractal analysis of Bernoulli convolutions associated with Salem numbers ⋮ The Assouad dimension of self-affine carpets with no grid structure ⋮ Multifractal formalism for almost all self-affine measures ⋮ Digit frequencies and self-affine sets with non-empty interior ⋮ Bifurcations of digit frequencies in unique expansions ⋮ The Two-Dimensional Density of Bernoulli Convolutions ⋮ Digit frequencies of beta-expansions ⋮ On the invariant density of the random \(\beta\)-transformation ⋮ On Furstenberg's intersection conjecture, self-similar measures, and the \(L^q\) norms of convolutions ⋮ On univoque and strongly univoque sets ⋮ Exceptional digit frequencies and expansions in non-integer bases ⋮ Numbers with simply normal β-expansions ⋮ Wave propagation speed on fractals ⋮ On the continuity of the Hausdorff dimension of the univoque set ⋮ Relative bifurcation sets and the local dimension of univoque bases ⋮ Multifractality of overlapping non-uniform self-similar measures

Cites Work

• Unnamed Item
• Multifractal formalism for self-similar measures with weak separation condition
• Infinite Bernoulli convolutions with different probabilities
• Multifractal decompositions of Moran fractals
• On the random series \(\sum\pm\lambda^ n\) (an Erdös problem)
• Absolute continuity of Bernoulli convolutions, a simple proof
• Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions
• On the Gibbs properties of Bernoulli convolutions related to \(\beta\)-numeration in multinacci bases
• Some exceptional phenomena in multifractal formalism. II
• Dimension theory of iterated function systems
• On theβ-expansions of real numbers
• A lower bound for the symbolic multifractal spectrum of a self-similar multifractal with arbitrary overlaps
• The equivalence of some Bernoulli convolutions to Lebesgue measure
• Self-similar measures and intersections of Cantor sets
• Unique Developments in Non-Integer Bases
• The local dimensions of the Bernoulli convolution associated with the golden number
• Random Self-Similar Multifractals
• Gibbs properties of self-conformal measures and the multifractal formalism
• Zeros of {-1, 0, 1} Power Series and Connectedness Loci for Self-Affine Sets
• Unique representations of real numbers in non-integer bases

This page was built for publication: Multifractal structure of Bernoulli convolutions