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.
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Arneodo, A., Grasseau, G., Holschneider, M. (1989). Wavelet Transform Analysis of Invariant Measures of Some Dynamical Systems. In: Combes, JM., Grossmann, A., Tchamitchian, P. (eds) Wavelets. Inverse Problems and Theoretical Imaging. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97177-8_15
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DOI: https://doi.org/10.1007/978-3-642-97177-8_15
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