96-245 Charles-Antoine GUERIN and Matthias HOLSCHNEIDER
Scattering on fractal measures. (389K, LATEX 209) Jun 4, 96
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Abstract. We study the one-dimensional potential-scattering problem when the potential is a Radon measure with compact support. We show that the usual reflection and transmission amplitude $r(p)$ and $t(p)$ of an incoming wave $e^{ipx}$ are well defined. We also show that the scattering problem on fractal potentials can be obtainded as a limit case of scattering on smooth potentials. We then explain how to retrieve the fractal 2-wavelet dimension and/or the correlation dimension of the potential by mean of the reflexion amplitude $r(p)$. We study the particular case of self-similar measures and show that, under some general conditions, $r(p)$ has a large scale renormalisation. A numerical application is presented.

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