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Article Dans Une Revue Physical Review Letters Année : 1995

Oscillating singularities in locally self-similar functions

Alain Arneodo
Jean-François Muzy

Résumé

Singularities induced by oscillating behavior are analyzed using the wavelet transform. We define two local exponents which allow us to characterize both the singularity strength (Hölder exponent) and the instantaneous frequency of the oscillations. Such oscillating singularities are shown to appear generically in local self-similar functions which are invariant under a nonhyperbolic mapping. We illustrate our results on both isolated singularities and nonisolated singularities appearing in fractal signals generated by nonhyperbolic iterative function systems.
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hal-01557134 , version 1 (05-07-2017)

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Alain Arneodo, Emmanuel Bacry, Jean-François Muzy. Oscillating singularities in locally self-similar functions. Physical Review Letters, 1995, 74 (24), pp.4823-4826. ⟨10.1103/PhysRevLett.74.4823⟩. ⟨hal-01557134⟩
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