Singularity spectrum of fractal signals from wavelet analysis: Exact results

DOI10.1007/BF01053588zbMath0943.37500MaRDI QIDQ1279188

Jean-François Muzy, Emmanuel Bacry, Alain Arneodo

Publication date: 4 September 2000

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

zbMATH Keywords

wavelet analysisinvariant measureswavelet transform modulus maximamultifractal formalismHölder exponentsfractal signals

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Ergodic theorems, spectral theory, Markov operators (37A30) Fractals (28A80) Dynamical aspects of statistical mechanics (37A60)

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Cites Work

• The infinite number of generalized dimensions of fractals and strange attractors
• Some characterizations of strange sets
• Dimensions and entropies of strange attractors from a fluctuating dynamics approach
• Les ondelettes en 1989. Séminaire d'analyse harmonique, Université de Paris-Sud, Orsay, France
• The dimension spectrum of some dynamical systems
• On the wavelet transformation of fractal objects.
• Scaling laws for invariant measures on hyperbolic and nonhyperbolic attractors.
• Velocity probability density functions of high Reynolds number turbulence
• Fractal measures and their singularities: The characterization of strange sets
• Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape
• Painless nonorthogonal expansions
• Singularity detection and processing with wavelets
• Wavelet analysis and synthesis of fractional Brownian motion
• Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier
• A simple dynamical model of intermittent fully developed turbulence
• The multifractal nature of turbulent energy dissipation
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