Oscillating singularities on Cantor sets: A grand-canonical multifractal formalism

DOI10.1007/BF02181485zbMath0917.28007OpenAlexW2071824960MaRDI QIDQ1285038

Stéphane Jaffard, Alain Arneodo, Emmanuel Bacry, Jean-François Muzy

Publication date: 26 April 1999

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02181485

zbMATH Keywords

wavelet analysisinvariant measuresminimizing sequenceswavelet transformCantor setsHölder exponentfractal functionscusp singularitiesoscillating singularitiessingularity spectrummodulus maximagrand-canonical multifractal formalismoscillation exponents

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Fractals (28A80)

Related Items (10)

Study of a robust feature: the pointwise Lipschitz regularity ⋮ The dimension of chaotic dynamical system in wavelet space and its application ⋮ A family of functions with two different spectra of singularities ⋮ The largest Lyapunov exponent of chaotic dynamical system in scale space and its application ⋮ A scale-space approach with wavelets to singularity estimation ⋮ Oscillation spaces: Properties and applications to fractal and multifractal functions ⋮ Random cascades on wavelet dyadic trees ⋮ Singularity spectrum of multifractal functions involving oscillating singularities ⋮ Two results concerning chirps and 2-microlocal exponents prescription ⋮ Wavelet analysis of fractal boundaries. I: Local exponents

Cites Work

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• Some characterizations of strange sets
• Wavelet transforms of self-similar processes
• Singularity spectrum of fractal signals from wavelet analysis: Exact results
• The dimension spectrum of some dynamical systems
• On the wavelet transformation of fractal objects.
• Fractal measures and their singularities: The characterization of strange sets
• Dimension, entropy and Lyapunov exponents
• Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape
• The singularity spectrumf(α) for cookie-cutters
• Singularity detection and processing with wavelets
• Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies
• Ten Lectures on Wavelets
• THE MULTIFRACTAL FORMALISM REVISITED WITH WAVELETS
• Wavelet analysis of a Gaussian Kolmogorov signal
• Multifractal Formalism for Functions Part I: Results Valid For All Functions
• BEYOND CLASSICAL MULTIFRACTAL ANALYSIS USING WAVELETS: UNCOVERING A MULTIPLICATIVE PROCESS HIDDEN IN THE GEOMETRICAL COMPLEXITY OF DIFFUSION LIMITED AGGREGATES
• Uncovering a multiplicative process in one-dimensional cuts of diffusion-limited aggregates
• Wavelet methods for pointwise regularity and local oscillations of functions

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