Multifractal structure of convolution of the Cantor measure

DOI10.1006/aama.2000.0683zbMath0991.28008OpenAlexW1994589293MaRDI QIDQ5953147

Ka-Sing Lau, Tian-You Hu

Publication date: 24 August 2002

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/4ce10ddbcf5deca940611fdabf077d58694fbe37

zbMATH Keywords

convolutionprobabilitylocal dimensionCantor measuremultifractalmultiple representation

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Fractals (28A80) Dimension theory of smooth dynamical systems (37C45)

Related Items (14)

Lyapunov exponents for products of matrices and multifractal analysis. II: General matrices ⋮ Eigenvalues and eigenfunctions of one-dimensional fractal Laplacians defined by iterated function systems with overlaps ⋮ Multifractal structure and product of matrices ⋮ Local dimensions of measures of finite type III -- measures that are not equicontractive ⋮ Geometric and combinatorial properties of self-similar multifractal measures ⋮ Local dimensions of overlapping self-similar measures ⋮ Local dimensions of self-similar measures satisfying the finite neighbour condition* ⋮ Bounds for the \(L^q\)-spectra of self-similar measures without any separation conditions ⋮ Measures and functions with prescribed homogeneous multifractal spectrum ⋮ Uniqueness of the measure with full dimension on sofic affine-invariant subsets of the 2-torus ⋮ On multifractal formalism for self-similar measures with overlaps ⋮ Multifractal formalism for self-similar measures with weak separation condition ⋮ Multifractal Analysis of Cantor-Like Measures ⋮ When the weak separation condition implies the generalized finite type condition

Cites Work

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• Multifractal decompositions of Moran fractals
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• The local dimensions of the Bernoulli convolution associated with the golden number
• On the Morphology of γ-Expansions with Deleted Digits
• The Hausdorff Dimension of λ-Expansions with Deleted Digits
• Iterated function systems with overlaps

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