Wavelets pp 182-196 | Cite as

Wavelet Transform Analysis of Invariant Measures of Some Dynamical Systems

  • A. Arneodo
  • G. Grasseau
  • M. Holschneider
Conference paper
Part of the Inverse Problems and Theoretical Imaging book series (IPTI)

Abstract

We present the wavelet transform as a mathematical microscope which is well suited for studying the local scaling properties of fractal measures. We apply this technique, recently introduced in signal analysis, to probability measures on self-similar Cantor sets, to the 2∞ cycle of period-doubling and to the golden-mean trajectories on two-tori at the onset of chaos. We emphasize the wide range of application of the wavelet transform which turns out to be a natural tool for characterizing the structural properties of fractal objects arising in a variety of physical situations.

Keywords

Invariant Measure Fractal Measure Fractal Object Fast Wavelet Transform Generalize Fractal Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • A. Arneodo
    • 1
    • 3
  • G. Grasseau
    • 1
  • M. Holschneider
    • 2
    • 4
  1. 1.Centre de Recherche Paul PascalDomaine UniversitaireTalence CedexFrance
  2. 2.Centre de Physique ThéoriqueCNRS LuminyMarseille CedexFrance
  3. 3.Laboratoire de Physique ThéoriqueUniversité de NiceNice CedexFrance
  4. 4.Mathematisches InstitutRuhr UniversitätBochum 1Fed. Rep. of Germany

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